On The Jacobson Radical Of A Group Algebra

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The Jacobson Radical of Group Algebras

Author : G. Karpilovsky
Publisher : Elsevier
ISBN 13 : 0080872468
Total Pages : 543 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis The Jacobson Radical of Group Algebras by : G. Karpilovsky

Download or read book The Jacobson Radical of Group Algebras written by G. Karpilovsky and published by Elsevier. This book was released on 1987-04-01 with total page 543 pages. Available in PDF, EPUB and Kindle. Book excerpt: Let G be a finite group and let F be a field. It is well known that linear representations of G over F can be interpreted as modules over the group algebra FG. Thus the investigation of ring-theoretic structure of the Jacobson radical J(FG) of FG is of fundamental importance. During the last two decades the subject has been pursued by a number of researchers and many interesting results have been obtained. This volume examines these results.The main body of the theory is presented, giving the central ideas, the basic results and the fundamental methods. It is assumed that the reader has had the equivalent of a standard first-year graduate algebra course, thus familiarity with basic ring-theoretic and group-theoretic concepts and an understanding of elementary properties of modules, tensor products and fields. A chapter on algebraic preliminaries is included, providing a survey of topics needed later in the book. There is a fairly large bibliography of works which are either directly relevant to the text or offer supplementary material of interest.

On the Jacobson Radical of a Group Algebra

Author : Ahmad Abdul Hadi Chalabi
Publisher :
ISBN 13 :
Total Pages : 86 pages
Book Rating : 4.:/5 (44 download)

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Book Synopsis On the Jacobson Radical of a Group Algebra by : Ahmad Abdul Hadi Chalabi

Download or read book On the Jacobson Radical of a Group Algebra written by Ahmad Abdul Hadi Chalabi and published by . This book was released on 1969 with total page 86 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Jacobson Radical of a Group Algebra

Author : Michael Ira Rosen
Publisher :
ISBN 13 :
Total Pages : 24 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Jacobson Radical of a Group Algebra by : Michael Ira Rosen

Download or read book The Jacobson Radical of a Group Algebra written by Michael Ira Rosen and published by . This book was released on 1965 with total page 24 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Jacobson Radical of Classical Rings

Author : Gregory Karpilovsky
Publisher :
ISBN 13 :
Total Pages : 592 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis The Jacobson Radical of Classical Rings by : Gregory Karpilovsky

Download or read book The Jacobson Radical of Classical Rings written by Gregory Karpilovsky and published by . This book was released on 1991 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to provide comprehensive coverage of the structure of the Jacobson radical of classical rings. Special attention is drawn to the discoveries concerning the Jacobson radical of graded rings. The main objective has been to present an accessible, self-contained and detailed coverage of the present state of the subject, so that the reader can find in one place all that is needed for a thorough understanding of the main results, along with concrete information on how the ideas are applied.

Rings and Their Modules

Author : Paul E. Bland
Publisher : Walter de Gruyter
ISBN 13 : 3110250225
Total Pages : 467 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Rings and Their Modules by : Paul E. Bland

Download or read book Rings and Their Modules written by Paul E. Bland and published by Walter de Gruyter. This book was released on 2011 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. In addition to the presentation of standard topics in ring and module theory, it also covers category theory, homological algebra and even more specialized topics like injective envelopes and proj

The Jacobson Radical of Classical Rings

Author : Gregory Karpilovsky
Publisher :
ISBN 13 : 9780608052335
Total Pages : 579 pages
Book Rating : 4.0/5 (523 download)

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Book Synopsis The Jacobson Radical of Classical Rings by : Gregory Karpilovsky

Download or read book The Jacobson Radical of Classical Rings written by Gregory Karpilovsky and published by . This book was released on 1991-01-01 with total page 579 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Finite Dimensional Algebras

Author : Yurj A. Drozd
Publisher : Springer Science & Business Media
ISBN 13 : 3642762441
Total Pages : 260 pages
Book Rating : 4.6/5 (427 download)

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Book Synopsis Finite Dimensional Algebras by : Yurj A. Drozd

Download or read book Finite Dimensional Algebras written by Yurj A. Drozd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: This English edition has an additional chapter "Elements of Homological Al gebra". Homological methods appear to be effective in many problems in the theory of algebras; we hope their inclusion makes this book more complete and self-contained as a textbook. We have also taken this occasion to correct several inaccuracies and errors in the original Russian edition. We should like to express our gratitude to V. Dlab who has not only metic ulously translated the text, but has also contributed by writing an Appendix devoted to a new important class of algebras, viz. quasi-hereditary algebras. Finally, we are indebted to the publishers, Springer-Verlag, for enabling this book to reach such a wide audience in the world of mathematical community. Kiev, February 1993 Yu.A. Drozd V.V. Kirichenko Preface The theory of finite dimensional algebras is one of the oldest branches of modern algebra. Its origin is linked to the work of Hamilton who discovered the famous algebra of quaternions, and Cayley who developed matrix theory. Later finite dimensional algebras were studied by a large number of mathematicians including B. Peirce, C.S. Peirce, Clifford, ·Weierstrass, Dedekind, Jordan and Frobenius. At the end of the last century T. Molien and E. Cartan described the semisimple algebras over the complex and real fields and paved the first steps towards the study of non-semi simple algebras.

Group and Semigroup Rings

Author : G. Karpilovsky
Publisher : Elsevier
ISBN 13 : 0080872379
Total Pages : 277 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Group and Semigroup Rings by : G. Karpilovsky

Download or read book Group and Semigroup Rings written by G. Karpilovsky and published by Elsevier. This book was released on 2011-09-22 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: A broad range of topics is covered here, including commutative monoid rings, the Jacobson radical of semigroup rings, blocks of modular group algebras, nilpotency index of the radical of group algebras, the isomorphism problem for group rings, inverse semigroup algebras and the Picard group of an abelian group ring. The survey lectures provide an up-to-date account of the current state of the subject and form a comprehensive introduction for intending researchers.

Induced Modules over Group Algebras

Author : G. Karpilovsky
Publisher : Elsevier
ISBN 13 : 0080872727
Total Pages : 533 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Induced Modules over Group Algebras by : G. Karpilovsky

Download or read book Induced Modules over Group Algebras written by G. Karpilovsky and published by Elsevier. This book was released on 1990-03-01 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1898 Frobenius discovered a construction which, in present terminology, associates with every module of a subgroup the induced module of a group. This construction proved to be of fundamental importance and is one of the basic tools in the entire theory of group representations.This monograph is designed for research mathematicians and advanced graduate students and gives a picture of the general theory of induced modules as it exists at present. Much of the material has until now been available only in research articles. The approach is not intended to be encyclopedic, rather each topic is considered in sufficient depth that the reader may obtain a clear idea of the major results in the area.After establishing algebraic preliminaries, the general facts about induced modules are provided, as well as some of their formal properties, annihilators and applications. The remaining chapters include detailed information on the process of induction from normal subgroups, projective summands of induced modules, some basic results of the Green theory with refinements and extensions, simple induction and restriction pairs and permutation modules. The final chapter is based exclusively on the work of Weiss, presenting a number of applications to the isomorphism problem for group rings.

Encyclopaedia of Mathematics

Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
ISBN 13 : 9400903650
Total Pages : 743 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Encyclopaedia of Mathematics by : Michiel Hazewinkel

Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 743 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.

Representation Theory II. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984

Download Representation Theory II. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984 PDF Online Free

Author : Vlastimil Dlab
Publisher : Springer
ISBN 13 : 3540397779
Total Pages : 386 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Representation Theory II. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984 by : Vlastimil Dlab

Download or read book Representation Theory II. Proceedings of the Fourth International Conference on Representations of Algebras, held in Ottawa, Canada, August 16-25, 1984 written by Vlastimil Dlab and published by Springer. This book was released on 2006-11-14 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Trends in Ring Theory

Author : Vlastimil Dlab
Publisher : American Mathematical Soc.
ISBN 13 : 9780821808498
Total Pages : 284 pages
Book Rating : 4.8/5 (84 download)

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Book Synopsis Trends in Ring Theory by : Vlastimil Dlab

Download or read book Trends in Ring Theory written by Vlastimil Dlab and published by American Mathematical Soc.. This book was released on 1998 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Ring Theory Conference, held a the University of Miskolc, Hungary, successfully accomplished its two goals: to reflect contemporary trends in the subject area; and to offer a meeting place for a large number of Eastern European algebraists and their colleagues from around the world. Particular emphasis was placed on recent developments in the following four areas: representation theory, group algebras, PI algebras and general ring theory. This book presents 13 of the invited lectures.

Infinite Groups: Geometric, Combinatorial and Dynamical Aspects

Author : Laurent Bartholdi
Publisher : Springer Science & Business Media
ISBN 13 : 3764374470
Total Pages : 419 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Infinite Groups: Geometric, Combinatorial and Dynamical Aspects by : Laurent Bartholdi

Download or read book Infinite Groups: Geometric, Combinatorial and Dynamical Aspects written by Laurent Bartholdi and published by Springer Science & Business Media. This book was released on 2006-03-28 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers a panorama of recent advances in the theory of infinite groups. It contains survey papers contributed by leading specialists in group theory and other areas of mathematics. Topics include amenable groups, Kaehler groups, automorphism groups of rooted trees, rigidity, C*-algebras, random walks on groups, pro-p groups, Burnside groups, parafree groups, and Fuchsian groups. The accent is put on strong connections between group theory and other areas of mathematics.

On unit groups of modular group algebras

Author : Sven Bodo Wirsing
Publisher : Anchor Academic Publishing
ISBN 13 : 3960677243
Total Pages : 200 pages
Book Rating : 4.9/5 (66 download)

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Book Synopsis On unit groups of modular group algebras by : Sven Bodo Wirsing

Download or read book On unit groups of modular group algebras written by Sven Bodo Wirsing and published by Anchor Academic Publishing. This book was released on 2019-12-16 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book we analyse unit groups of group algebras KG for non-abelian p-groups G and fields K of characteristic p. By calculating the core and the normaliser of U in 1 + rad(KG) – the group of normalized units -- for every subgroup U of G, we generalise results of K.R. Pearson and D.B. Coleman using fixed points of enhanced group actions. Our concept of so-called end-commutable ordering leads to a new method of studying the center of 1 + rad(KG). We proof that a finite group G is nilpotent if and only if every conjugacy class possesses an end-commutable ordering. As a simple consequence we get a result of A.A. Bovdi and Z. Patay, which shows how the exponent of the center of 1 + rad(KG) can be determined by calculations purely within the group G. We describe the groups for which this exponent is extremal and calculate the exponent for various group classes (e.g. regular groups, special groups, Sylow subgroups of linear and symmetric groups) and group constructions (e.g. wreath products, central products, special group extensions, isoclinic groups). Another application of our concept of end-commutable ordering is a description of the invariants of the center of 1 + rad(KG) for a finite field K. They are determined purely by the group G and the field K and can be visualized by a special graph – the class-graph. As a consequence of our results we prove that the center, the derived subgroups and the p-th-power subgroup of 1 + rad(KG) are not cyclic. Furthermore, we obtain some properties of unit groups of group algebras for extra-special 2-groups and fields of characteristic 2. Finally, we investigate the behaviour of the center and other characteristics (e.g. the exponent, the class of nilpotency, the Baer length, the degree of commutativity) for the chain of iterated unit groups of modular group algebras. For this, we use Lie and radical algebra methods.

Relative Projectivity and Radicals in Modular Group Algebras

Author : Dharam Chand Khatri
Publisher :
ISBN 13 :
Total Pages : 118 pages
Book Rating : 4.3/5 (129 download)

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Book Synopsis Relative Projectivity and Radicals in Modular Group Algebras by : Dharam Chand Khatri

Download or read book Relative Projectivity and Radicals in Modular Group Algebras written by Dharam Chand Khatri and published by . This book was released on 1972 with total page 118 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Scientific and Technical Aerospace Reports

Author :
Publisher :
ISBN 13 :
Total Pages : 1336 pages
Book Rating : 4.:/5 (319 download)

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Book Synopsis Scientific and Technical Aerospace Reports by :

Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1967 with total page 1336 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Modern Algebra

Author : Joseph J. Rotman
Publisher : American Mathematical Soc.
ISBN 13 : 0821847414
Total Pages : 1026 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Advanced Modern Algebra by : Joseph J. Rotman

Download or read book Advanced Modern Algebra written by Joseph J. Rotman and published by American Mathematical Soc.. This book was released on 2010-08-11 with total page 1026 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is designed as a text for the first year of graduate algebra, but it can also serve as a reference since it contains more advanced topics as well. This second edition has a different organization than the first. It begins with a discussion of the cubic and quartic equations, which leads into permutations, group theory, and Galois theory (for finite extensions; infinite Galois theory is discussed later in the book). The study of groups continues with finite abelian groups (finitely generated groups are discussed later, in the context of module theory), Sylow theorems, simplicity of projective unimodular groups, free groups and presentations, and the Nielsen-Schreier theorem (subgroups of free groups are free). The study of commutative rings continues with prime and maximal ideals, unique factorization, noetherian rings, Zorn's lemma and applications, varieties, and Gr'obner bases. Next, noncommutative rings and modules are discussed, treating tensor product, projective, injective, and flat modules, categories, functors, and natural transformations, categorical constructions (including direct and inverse limits), and adjoint functors. Then follow group representations: Wedderburn-Artin theorems, character theory, theorems of Burnside and Frobenius, division rings, Brauer groups, and abelian categories. Advanced linear algebra treats canonical forms for matrices and the structure of modules over PIDs, followed by multilinear algebra. Homology is introduced, first for simplicial complexes, then as derived functors, with applications to Ext, Tor, and cohomology of groups, crossed products, and an introduction to algebraic K-theory. Finally, the author treats localization, Dedekind rings and algebraic number theory, and homological dimensions. The book ends with the proof that regular local rings have unique factorization."--Publisher's description.