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Author : E. S. Li͡apin
Publisher :
ISBN 13 :
Total Pages : 60 pages
Book Rating : 4.X/5 (1 download)
Download or read book On the Decomposition of Abelian Groups Into Direct Sums of Rational Groups written by E. S. Li͡apin and published by . This book was released on 1950 with total page 60 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : E. Li︠a︡pin
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (636 download)
Download or read book On the Decomposition of Abelian Groups Into Direct Sums of Rational Groups written by E. Li︠a︡pin and published by . This book was released on 1950 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : E. S. Li︠a︡pin
Publisher :
ISBN 13 :
Total Pages : 56 pages
Book Rating : 4.:/5 (464 download)
Download or read book On the Decomposition of Abelian Groups Into Direct Sums of Rational Groups written by E. S. Li︠a︡pin and published by . This book was released on 1950 with total page 56 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : A Mader
Publisher : CRC Press
ISBN 13 : 148228748X
Total Pages : 366 pages
Book Rating : 4.4/5 (822 download)
Download or read book Almost Completely Decomposable Groups written by A Mader and published by CRC Press. This book was released on 2000-03-09 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt: An almost completely decomposable abelian (acd) group is an extension of a finite direct sum of subgroups of the additive group of rational numbers by a finite abelian group. Examples are easy to write and are frequently used but have been notoriously difficult to study and classify because of their computational nature. However, a general theory o
Author : L. Fuchs
Publisher : Elsevier
ISBN 13 : 148328090X
Total Pages : 369 pages
Book Rating : 4.4/5 (832 download)
Download or read book Abelian Groups written by L. Fuchs and published by Elsevier. This book was released on 2014-07-15 with total page 369 pages. Available in PDF, EPUB and Kindle. Book excerpt: Abelian Groups deals with the theory of abelian or commutative groups, with special emphasis on results concerning structure problems. More than 500 exercises of varying degrees of difficulty, with and without hints, are included. Some of the exercises illuminate the theorems cited in the text by providing alternative developments, proofs or counterexamples of generalizations. Comprised of 16 chapters, this volume begins with an overview of the basic facts on group theory such as factor group or homomorphism. The discussion then turns to direct sums of cyclic groups, divisible groups, and direct summands and pure subgroups, as well as Kulikov's basic subgroups. Subsequent chapters focus on the structure theory of the three main classes of abelian groups: the primary groups, the torsion-free groups, and the mixed groups. Applications of the theory are also considered, along with other topics such as homomorphism groups and endomorphism rings; the Schreier extension theory with a discussion of the group of extensions and the structure of the tensor product. In addition, the book examines the theory of the additive group of rings and the multiplicative group of fields, along with Baer's theory of the lattice of subgroups. This book is intended for young research workers and students who intend to familiarize themselves with abelian groups.
Author : Irving Kaplansky
Publisher : Courier Dover Publications
ISBN 13 : 0486836452
Total Pages : 112 pages
Book Rating : 4.4/5 (868 download)
Download or read book Infinite Abelian Groups written by Irving Kaplansky and published by Courier Dover Publications. This book was released on 2018-12-19 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: This concise monograph presents the theory of infinite abelian groups in a convenient form and helps students acquire some of the techniques used in modern infinite algebra. 1969 edition.
Author : Vyacheslav L. Girko
Publisher : Academic Press
ISBN 13 : 0080873499
Total Pages : 375 pages
Book Rating : 4.0/5 (88 download)
Download or read book Spectral Theory of Random Matrices written by Vyacheslav L. Girko and published by Academic Press. This book was released on 2016-08-23 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: Spectral Theory of Random Matrices
Author : D. Valcan
Publisher : Springer Science & Business Media
ISBN 13 : 9401703396
Total Pages : 353 pages
Book Rating : 4.4/5 (17 download)
Download or read book Exercises in Abelian Group Theory written by D. Valcan and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, in some sense, began to be written by the first author in 1983, when optional lectures on Abelian groups were held at the Fac ulty of Mathematics and Computer Science,'Babes-Bolyai' University in Cluj-Napoca, Romania. From 1992,these lectures were extended to a twosemester electivecourse on abelian groups for undergraduate stu dents, followed by a twosemester course on the same topic for graduate students in Algebra. All the other authors attended these two years of lectures and are now Assistants to the Chair of Algebra of this Fac ulty. The first draft of this collection, including only exercises solved by students as home works, the last ten years, had 160pages. We felt that there is a need for a book such as this one, because it would provide a nice bridge between introductory Abelian Group Theory and more advanced research problems. The book InfiniteAbelianGroups, published by LaszloFuchsin two volumes 1970 and 1973 willwithout doubt last as the most important guide for abelian group theorists. Many exercises are selected from this source but there are plenty of other bibliographical items (see the Bibliography) which were used in order to make up this collection. For some of the problems stated, recent developments are also given. Nevertheless, there are plenty of elementary results (the so called 'folklore') in Abelian Group Theory whichdo not appear in any written material. It is also one purpose of this book to complete this gap.
Author : Laszlo Fuchs
Publisher : CRC Press
ISBN 13 : 100011676X
Total Pages : 280 pages
Book Rating : 4.0/5 (1 download)
Download or read book Abelian Groups written by Laszlo Fuchs and published by CRC Press. This book was released on 2022-01-27 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains information offered at the international conference held in Curacao, Netherlands Antilles. It presents the latest developments in the most active areas of abelian groups, particularly in torsion-free abelian groups.;For both researchers and graduate students, it reflects the current status of abelian group theory.;Abelian Groups discusses: finite rank Butler groups; almost completely decomposable groups; Butler groups of infinite rank; equivalence theorems for torsion-free groups; cotorsion groups; endomorphism algebras; and interactions of set theory and abelian groups.;This volume contains contributions from international experts. It is aimed at algebraists and logicians, research mathematicians, and advanced graduate students in these disciplines.
Author : Christopher Norman
Publisher : Springer Science & Business Media
ISBN 13 : 1447127307
Total Pages : 389 pages
Book Rating : 4.4/5 (471 download)
Download or read book Finitely Generated Abelian Groups and Similarity of Matrices over a Field written by Christopher Norman and published by Springer Science & Business Media. This book was released on 2012-01-25 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: At first sight, finitely generated abelian groups and canonical forms of matrices appear to have little in common. However, reduction to Smith normal form, named after its originator H.J.S.Smith in 1861, is a matrix version of the Euclidean algorithm and is exactly what the theory requires in both cases. Starting with matrices over the integers, Part 1 of this book provides a measured introduction to such groups: two finitely generated abelian groups are isomorphic if and only if their invariant factor sequences are identical. The analogous theory of matrix similarity over a field is then developed in Part 2 starting with matrices having polynomial entries: two matrices over a field are similar if and only if their rational canonical forms are equal. Under certain conditions each matrix is similar to a diagonal or nearly diagonal matrix, namely its Jordan form. The reader is assumed to be familiar with the elementary properties of rings and fields. Also a knowledge of abstract linear algebra including vector spaces, linear mappings, matrices, bases and dimension is essential, although much of the theory is covered in the text but from a more general standpoint: the role of vector spaces is widened to modules over commutative rings. Based on a lecture course taught by the author for nearly thirty years, the book emphasises algorithmic techniques and features numerous worked examples and exercises with solutions. The early chapters form an ideal second course in algebra for second and third year undergraduates. The later chapters, which cover closely related topics, e.g. field extensions, endomorphism rings, automorphism groups, and variants of the canonical forms, will appeal to more advanced students. The book is a bridge between linear and abstract algebra.
Author : Carol Jacoby
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110427680
Total Pages : 342 pages
Book Rating : 4.1/5 (14 download)
Download or read book Abelian Groups written by Carol Jacoby and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-22 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph covers in a comprehensive manner the current state of classification theory with respect to infinite abelian groups. A wide variety of ways to characterise different classes of abelian groups by invariants, isomorphisms and duality principles are discussed.
Author : S. N. Cernikov
Publisher : American Mathematical Soc.
ISBN 13 : 9780821816011
Total Pages : 486 pages
Book Rating : 4.8/5 (16 download)
Download or read book Algebra written by S. N. Cernikov and published by American Mathematical Soc.. This book was released on 1962 with total page 486 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher : Academic Press
ISBN 13 : 0080873480
Total Pages : 305 pages
Book Rating : 4.0/5 (88 download)
Download or read book Infinite Abelian Groups written by and published by Academic Press. This book was released on 1970-01-01 with total page 305 pages. Available in PDF, EPUB and Kindle. Book excerpt: Infinite Abelian Groups
Author : Theodore G. Faticoni
Publisher : CRC Press
ISBN 13 : 9781584887270
Total Pages : 344 pages
Book Rating : 4.8/5 (872 download)
Download or read book Direct Sum Decompositions of Torsion-Free Finite Rank Groups written by Theodore G. Faticoni and published by CRC Press. This book was released on 2007-03-28 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: With plenty of new material not found in other books, Direct Sum Decompositions of Torsion-Free Finite Rank Groups explores advanced topics in direct sum decompositions of abelian groups and their consequences. The book illustrates a new way of studying these groups while still honoring the rich history of unique direct sum decompositions of groups
Author : László Fuchs
Publisher : Springer
ISBN 13 : 3319194224
Total Pages : 762 pages
Book Rating : 4.3/5 (191 download)
Download or read book Abelian Groups written by László Fuchs and published by Springer. This book was released on 2015-12-12 with total page 762 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by one of the subject’s foremost experts, this book focuses on the central developments and modern methods of the advanced theory of abelian groups, while remaining accessible, as an introduction and reference, to the non-specialist. It provides a coherent source for results scattered throughout the research literature with lots of new proofs. The presentation highlights major trends that have radically changed the modern character of the subject, in particular, the use of homological methods in the structure theory of various classes of abelian groups, and the use of advanced set-theoretical methods in the study of un decidability problems. The treatment of the latter trend includes Shelah’s seminal work on the un decidability in ZFC of Whitehead’s Problem; while the treatment of the former trend includes an extensive (but non-exhaustive) study of p-groups, torsion-free groups, mixed groups and important classes of groups arising from ring theory. To prepare the reader to tackle these topics, the book reviews the fundamentals of abelian group theory and provides some background material from category theory, set theory, topology and homological algebra. An abundance of exercises are included to test the reader’s comprehension, and to explore noteworthy extensions and related sidelines of the main topics. A list of open problems and questions, in each chapter, invite the reader to take an active part in the subject’s further development.
Author : László Fuchs
Publisher :
ISBN 13 :
Total Pages : 384 pages
Book Rating : 4.:/5 (31 download)
Download or read book Infinite Abelian Groups written by László Fuchs and published by . This book was released on 1970 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Alexandre Borovik
Publisher : American Mathematical Soc.
ISBN 13 : 0821836188
Total Pages : 360 pages
Book Rating : 4.8/5 (218 download)
Download or read book Groups, Languages, Algorithms written by Alexandre Borovik and published by American Mathematical Soc.. This book was released on 2005 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since the pioneering works of Novikov and Maltsev, group theory has been a testing ground for mathematical logic in its many manifestations, from the theory of algorithms to model theory. The interaction between logic and group theory led to many prominent results which enriched both disciplines. This volume reflects the major themes of the American Mathematical Society/Association for Symbolic Logic Joint Special Session (Baltimore, MD), Interactions between Logic, Group Theory and Computer Science. Included are papers devoted to the development of techniques used for the interaction of group theory and logic. It is suitable for graduate students and researchers interested in algorithmic and combinatorial group theory. A complement to this work is Volume 349 in the AMS series, Contemporary Mathematics, Computational and Experimental Group Theory, which arose from the same meeting and concentrates on the interaction of group theory and computer science.
