Separability Within Commutative And Solvable Associative Algebras Under Consideration Of Non Unitary Algebras With 401 Exercises

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Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises

Author : Sven Bodo Wirsing
Publisher : Anchor Academic Publishing
ISBN 13 : 3960677219
Total Pages : 257 pages
Book Rating : 4.9/5 (66 download)

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Book Synopsis Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises by : Sven Bodo Wirsing

Download or read book Separability within commutative and solvable associative algebras. Under consideration of non-unitary algebras. With 401 exercises written by Sven Bodo Wirsing and published by Anchor Academic Publishing. This book was released on 2018-12-12 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within the context of the Wedderburn-Malcev theorem a radical complement exists and all complements are conjugated. The main topics of this work are to analyze the Determination of a (all) radical complements, the representation of an element as the sum of a nilpotent and fully separable element and the compatibility of the Wedderburn-Malcev theorem with derived structures. Answers are presented in details for commutative and solvable associative algebras. Within the analysis the set of fully-separable elements and the generalized Jordan decomposition are of special interest. We provide examples based on generalized quaternion algebras, group algebras and algebras of traingular matrices over a field. The results (and also the theorem of Wedderburn-Malcev and Taft) are transferred to non-unitary algebras by using the star-composition and the adjunction of an unit. Within the App endix we present proofs for the Wedderburn-Malcev theorem for unitary algebras, for Taft's theorem on G-invariant radical complements for unitary algebras and for a theorem of Bauer concerning solvable unit groups of associative algebras.

Maximal nilpotent subalgebras II: A correspondence theorem within solvable associative algebras. With 242 exercises

Author : Sven Bodo Wirsing
Publisher : Anchor Academic Publishing
ISBN 13 : 3960676964
Total Pages : 193 pages
Book Rating : 4.9/5 (66 download)

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Book Synopsis Maximal nilpotent subalgebras II: A correspondence theorem within solvable associative algebras. With 242 exercises by : Sven Bodo Wirsing

Download or read book Maximal nilpotent subalgebras II: A correspondence theorem within solvable associative algebras. With 242 exercises written by Sven Bodo Wirsing and published by Anchor Academic Publishing. This book was released on 2017-11-09 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: Within series II we extend the theory of maximal nilpotent substructures to solvable associative algebras, especially for their group of units and their associated Lie algebra. We construct all maximal nilpotent Lie subalgebras and characterize them by simple and double centralizer properties. They possess distinctive attractor and repeller characteristics. Their number of isomorphic classes is finite and can be bounded by Bell numbers. Cartan subalgebras and the Lie nilradical are extremal among all maximal nilpotent Lie subalgebras. The maximal nilpotent Lie subalgebras are connected to the maximal nilpotent subgroups. This correspondence is bijective via forming the group of units and creating the linear span. Cartan subalgebras and Carter subgroups as well as the Lie nilradical and the Fitting subgroup are linked by this correspondence. All partners possess the same class of nilpotency based on a theorem of Xiankun Du. By using this correspondence we transfer all results to maximal nilpotent subgroups of the group of units. Carter subgroups and the Fitting subgroup turn out to be extremal among all maximal nilpotent subgroups. All four extremal substructures are proven to be Fischer subgroups, Fischer subalgebras, nilpotent injectors and projectors. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory.

Non-Associative Normed Algebras: Volume 2, Representation Theory and the Zel'manov Approach

Author : Miguel Cabrera García
Publisher : Cambridge University Press
ISBN 13 : 1108570763
Total Pages : 759 pages
Book Rating : 4.1/5 (85 download)

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Book Synopsis Non-Associative Normed Algebras: Volume 2, Representation Theory and the Zel'manov Approach by : Miguel Cabrera García

Download or read book Non-Associative Normed Algebras: Volume 2, Representation Theory and the Zel'manov Approach written by Miguel Cabrera García and published by Cambridge University Press. This book was released on 2018-04-12 with total page 759 pages. Available in PDF, EPUB and Kindle. Book excerpt: This first systematic account of the basic theory of normed algebras, without assuming associativity, includes many new and unpublished results and is sure to become a central resource for researchers and graduate students in the field. This second volume revisits JB*-triples, covers Zel'manov's celebrated work in Jordan theory, proves the unit-free variant of the Vidav–Palmer theorem, and develops the representation theory of alternative C*-algebras and non-commutative JB*-algebras. This completes the work begun in the first volume, which introduced these algebras and discussed the so-called non-associative Gelfand–Naimark and Vidav–Palmer theorems. This book interweaves pure algebra, geometry of normed spaces, and infinite-dimensional complex analysis. Novel proofs are presented in complete detail at a level accessible to graduate students. The book contains a wealth of historical comments, background material, examples, and an extensive bibliography.

Separable Algebras over Commutative Rings

Author : Frank De Meyer
Publisher : Springer
ISBN 13 : 3540364846
Total Pages : 162 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Separable Algebras over Commutative Rings by : Frank De Meyer

Download or read book Separable Algebras over Commutative Rings written by Frank De Meyer and published by Springer. This book was released on 2006-11-15 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lecture notes were prepared by the authors for use in graduate courses and seminars, based on the work of many earlier mathematicians. In addition to very elementary results, presented for the convenience of the reader, Chapter I contains the Morita theorems and the definition of the projective class group of a commutative ring. Chapter II addresses the Brauer group of a commutative ring, and automorphisms of separable algebras. Chapter III surveys the principal theorems of the Galois theory for commutative rings. In Chapter IV the authors present a direct derivation of the first six terms of the seven-term exact sequence for Galois cohomology. In the fifth and final chapter the authors illustrate the preceding material with applications to the structure of central simple algebras and the Brauer group of a Dedekind domain, and they pose problems for further investigation. Exercises are included at the end of each chapter.

Maximal Nilpotent Subalgebras I: Nilradicals and Cartan Subalgebras in Associative Algebras. With 428 Exercises

Author : Sven Bodo Wirsing
Publisher : Anchor Academic Publishing
ISBN 13 : 3960671032
Total Pages : 245 pages
Book Rating : 4.9/5 (66 download)

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Book Synopsis Maximal Nilpotent Subalgebras I: Nilradicals and Cartan Subalgebras in Associative Algebras. With 428 Exercises by : Sven Bodo Wirsing

Download or read book Maximal Nilpotent Subalgebras I: Nilradicals and Cartan Subalgebras in Associative Algebras. With 428 Exercises written by Sven Bodo Wirsing and published by Anchor Academic Publishing. This book was released on 2016-12 with total page 245 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the author’s doctorate time at the Christian-Albrechts-Universitat to Kiel, Salvatore Siciliano gave a stimulating talk in the upper seminar algebra theory about Cartan subalgebras in Lie algebra associates to associative algebra. This talk was the incentive for the author to analyze maximal nilpotent substructures of the Lie algebra associated to associative algebras. In the present work Siciliano's theory about Cartan subalgebras is worked off and expanded to different special associative algebra classes. In addition, a second maximal nilpotent substructure is analyzed: the nilradical. Within this analysis the main focus is to describe these substructure with the associative structure of the underlying algebra. This is successfully realized in this work. Numerous examples (like group algebras and Solomon (Tits-) algebras) illustrate the results to the reader. Within the numerous exercises these results can be applied by the reader to get a deeper insight in this theory.

Progress in Commutative Algebra 2

Author : Christopher Francisco
Publisher : Walter de Gruyter
ISBN 13 : 311027860X
Total Pages : 329 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Progress in Commutative Algebra 2 by : Christopher Francisco

Download or read book Progress in Commutative Algebra 2 written by Christopher Francisco and published by Walter de Gruyter. This book was released on 2012-04-26 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes of a state-of-the-art survey article collection which originates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. These volumes present current trends in two of the most active areas of commutative algebra: non-noetherian rings (factorization, ideal theory, integrality), and noetherian rings (the local theory, graded situation, and interactions with combinatorics and geometry). This volume contains surveys on aspects of closure operations, finiteness conditions and factorization. Closure operations on ideals and modules are a bridge between noetherian and nonnoetherian commutative algebra. It contains a nice guide to closure operations by Epstein, but also contains an article on test ideals by Schwede and Tucker and one by Enescu which discusses the action of the Frobenius on finite dimensional vector spaces both of which are related to tight closure. Finiteness properties of rings and modules or the lack of them come up in all aspects of commutative algebra. However, in the study of non-noetherian rings it is much easier to find a ring having a finite number of prime ideals. The editors have included papers by Boynton and Sather-Wagstaff and by Watkins that discuss the relationship of rings with finite Krull dimension and their finite extensions. Finiteness properties in commutative group rings are discussed in Glaz and Schwarz's paper. And Olberding's selection presents us with constructions that produce rings whose integral closure in their field of fractions is not finitely generated. The final three papers in this volume investigate factorization in a broad sense. The first paper by Celikbas and Eubanks-Turner discusses the partially ordered set of prime ideals of the projective line over the integers. The editors have also included a paper on zero divisor graphs by Coykendall, Sather-Wagstaff, Sheppardson and Spiroff. The final paper, by Chapman and Krause, concerns non-unique factorization.

An Introduction to Nonassociative Algebras

Author : Richard Donald Schafer
Publisher :
ISBN 13 :
Total Pages : 184 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis An Introduction to Nonassociative Algebras by : Richard Donald Schafer

Download or read book An Introduction to Nonassociative Algebras written by Richard Donald Schafer and published by . This book was released on 1966 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: Concise study presents in a short space some of the important ideas and results in the theory of nonassociative algebras, with particular emphasis on alternative and (commutative) Jordan algebras.

Non-Associative Algebra and Its Applications

Author : Lev Sabinin
Publisher : CRC Press
ISBN 13 : 1420003453
Total Pages : 553 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Non-Associative Algebra and Its Applications by : Lev Sabinin

Download or read book Non-Associative Algebra and Its Applications written by Lev Sabinin and published by CRC Press. This book was released on 2006-01-13 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: With contributions derived from presentations at an international conference, Non-Associative Algebra and Its Applications explores a wide range of topics focusing on Lie algebras, nonassociative rings and algebras, quasigroups, loops, and related systems as well as applications of nonassociative algebra to geometry, physics, and natural sciences.

On Normalized Integral Table Algebras (Fusion Rings)

Author : Zvi Arad
Publisher : Springer Science & Business Media
ISBN 13 : 085729850X
Total Pages : 279 pages
Book Rating : 4.8/5 (572 download)

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Book Synopsis On Normalized Integral Table Algebras (Fusion Rings) by : Zvi Arad

Download or read book On Normalized Integral Table Algebras (Fusion Rings) written by Zvi Arad and published by Springer Science & Business Media. This book was released on 2011-07-20 with total page 279 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of table algebras was introduced in 1991 by Z. Arad and H. Blau in order to treat, in a uniform way, products of conjugacy classes and irreducible characters of finite groups. Today, table algebra theory is a well-established branch of modern algebra with various applications, including the representation theory of finite groups, algebraic combinatorics and fusion rules algebras. This book presents the latest developments in this area. Its main goal is to give a classification of the Normalized Integral Table Algebras (Fusion Rings) generated by a faithful non-real element of degree 3. Divided into 4 parts, the first gives an outline of the classification approach, while remaining parts separately treat special cases that appear during classification. A particularly unique contribution to the field, can be found in part four, whereby a number of the algebras are linked to the polynomial irreducible representations of the group SL3(C). This book will be of interest to research mathematicians and PhD students working in table algebras, group representation theory, algebraic combinatorics and integral fusion rule algebras.

Topics in Noncommutative Algebra

Author : Andrea Bonfiglioli
Publisher : Springer Science & Business Media
ISBN 13 : 3642225969
Total Pages : 554 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Topics in Noncommutative Algebra by : Andrea Bonfiglioli

Download or read book Topics in Noncommutative Algebra written by Andrea Bonfiglioli and published by Springer Science & Business Media. This book was released on 2011-10-12 with total page 554 pages. Available in PDF, EPUB and Kindle. Book excerpt: Motivated by the importance of the Campbell, Baker, Hausdorff, Dynkin Theorem in many different branches of Mathematics and Physics (Lie group-Lie algebra theory, linear PDEs, Quantum and Statistical Mechanics, Numerical Analysis, Theoretical Physics, Control Theory, sub-Riemannian Geometry), this monograph is intended to: fully enable readers (graduates or specialists, mathematicians, physicists or applied scientists, acquainted with Algebra or not) to understand and apply the statements and numerous corollaries of the main result, provide a wide spectrum of proofs from the modern literature, comparing different techniques and furnishing a unifying point of view and notation, provide a thorough historical background of the results, together with unknown facts about the effective early contributions by Schur, Poincaré, Pascal, Campbell, Baker, Hausdorff and Dynkin, give an outlook on the applications, especially in Differential Geometry (Lie group theory) and Analysis (PDEs of subelliptic type) and quickly enable the reader, through a description of the state-of-art and open problems, to understand the modern literature concerning a theorem which, though having its roots in the beginning of the 20th century, has not ceased to provide new problems and applications. The book assumes some undergraduate-level knowledge of algebra and analysis, but apart from that is self-contained. Part II of the monograph is devoted to the proofs of the algebraic background. The monograph may therefore provide a tool for beginners in Algebra.

Introduction to Noncommutative Algebra

Author : Linsen Chou
Publisher :
ISBN 13 : 9781681171883
Total Pages : 0 pages
Book Rating : 4.1/5 (718 download)

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Book Synopsis Introduction to Noncommutative Algebra by : Linsen Chou

Download or read book Introduction to Noncommutative Algebra written by Linsen Chou and published by . This book was released on 2015-08 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: A noncommutative algebra is an associative algebra in which the multiplication is not commutative, that is, for which xy does not always equal yx; or more generally an algebraic structure in which one of the principal binary operations is not commutative; one also allows additional structures, e.g. topology or norm, to be possibly carried by the noncommutative algebra of functions. The main motivation is to extend the commutative duality between spaces and functions to the noncommutative setting. In mathematics, spaces, which are geometric in nature, can be related to numerical functions on them. In general, such functions will form a commutative ring. For instance, one may take the ring C(X) of continuous complex-valued functions on a topological space X. In many cases, we can recover X from C(X), and therefore it makes some sense to say that X has commutative topology. The dream of noncommutative geometry is to generalize this duality to the duality between noncommutative algebras, or sheaves of noncommutative algebras, or sheaf-like noncommutative algebraic or operator-algebraic structures and geometric entities of certain kind, and interact between the algebraic and geometric description of those via this duality. Regarding that the commutative rings correspond to usual affine schemes, and commutative C*-algebras to usual topological spaces, the extension to noncommutative rings and algebras requires non-trivial generalization of topological spaces, as "non-commutative spaces". This book provides an elementary introduction to noncommutative rings and algebras.

Non-commutative Algebraic Geometry

Author : F. Van Oystaeyen
Publisher : Lecture Notes in Mathematics
ISBN 13 :
Total Pages : 420 pages
Book Rating : 4.F/5 ( download)

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Book Synopsis Non-commutative Algebraic Geometry by : F. Van Oystaeyen

Download or read book Non-commutative Algebraic Geometry written by F. Van Oystaeyen and published by Lecture Notes in Mathematics. This book was released on 1981-10 with total page 420 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Some Non-associative Algebras in which the Multiplication of Indices is Commutative

Author : I. M. H. Etherington
Publisher :
ISBN 13 :
Total Pages : 55 pages
Book Rating : 4.:/5 (116 download)

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Book Synopsis Some Non-associative Algebras in which the Multiplication of Indices is Commutative by : I. M. H. Etherington

Download or read book Some Non-associative Algebras in which the Multiplication of Indices is Commutative written by I. M. H. Etherington and published by . This book was released on 1941 with total page 55 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Non-commutative Multiple-Valued Logic Algebras

Author : Lavinia Corina Ciungu
Publisher : Springer
ISBN 13 : 9783319015903
Total Pages : 276 pages
Book Rating : 4.0/5 (159 download)

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Book Synopsis Non-commutative Multiple-Valued Logic Algebras by : Lavinia Corina Ciungu

Download or read book Non-commutative Multiple-Valued Logic Algebras written by Lavinia Corina Ciungu and published by Springer. This book was released on 2013-11-27 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides a self-contained and easy-to-read introduction to non-commutative multiple-valued logic algebras; a subject which has attracted much interest in the past few years because of its impact on information science, artificial intelligence and other subjects. A study of the newest results in the field, the monograph includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, pseudo-MTL algebras, pseudo-BL algebras and pseudo-MV algebras. It provides a fresh perspective on new trends in logic and algebras in that algebraic structures can be developed into fuzzy logics which connect quantum mechanics, mathematical logic, probability theory, algebra and soft computing. Written in a clear, concise and direct manner, Non-Commutative Multiple-Valued Logic Algebras will be of interest to masters and PhD students, as well as researchers in mathematical logic and theoretical computer science.

Progress in commutative algebra

Author : Sean Sather-Wagstaff
Publisher : Walter de Gruyter
ISBN 13 : 9783110278613
Total Pages : 315 pages
Book Rating : 4.2/5 (786 download)

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Book Synopsis Progress in commutative algebra by : Sean Sather-Wagstaff

Download or read book Progress in commutative algebra written by Sean Sather-Wagstaff and published by Walter de Gruyter. This book was released on 2012-04-13 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions atthe 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This second volume discusses closures, decompositions, and factorization.

Ideals of Identities of Associative Algebras

Author : Aleksandr Robertovich Kemer
Publisher : American Mathematical Soc.
ISBN 13 : 9780821845486
Total Pages : 81 pages
Book Rating : 4.8/5 (454 download)

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Book Synopsis Ideals of Identities of Associative Algebras by : Aleksandr Robertovich Kemer

Download or read book Ideals of Identities of Associative Algebras written by Aleksandr Robertovich Kemer and published by American Mathematical Soc.. This book was released on 1991 with total page 81 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book concerns the study of the structure of identities of PI-algebras over a field of characteristic zero. In the first chapter, the author brings out the connection between varieties of algebras and finitely-generated superalgebras. The second chapter examines graded identities of finitely-generated PI-superalgebras. One of the results proved concerns the decomposition of T-ideals, which is very useful for the study of specific varieties. In the fifth section of Chapter Two, the author solves Specht's problem, which asks whether every associative algebra over a field of characteristic zero has a finite basis of identities. The book closes with an application of methods and results established earlier: the author finds asymptotic bases of identities of algebras with unity satisfying all of the identities of the full algebra of matrices of order two.

Progress in commutative algebra: Combinatorics and homology

Author : Sean Sather-Wagstaff
Publisher : de Gruyter
ISBN 13 : 9783110250343
Total Pages : 361 pages
Book Rating : 4.2/5 (53 download)

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Book Synopsis Progress in commutative algebra: Combinatorics and homology by : Sean Sather-Wagstaff

Download or read book Progress in commutative algebra: Combinatorics and homology written by Sean Sather-Wagstaff and published by de Gruyter. This book was released on 2012 with total page 361 pages. Available in PDF, EPUB and Kindle. Book excerpt: Annotation This is the first of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University meeting. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This fist volume concentrates on combinatorics and homology.