finitely generated abelian groups and similarity of matrices over a field

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Finitely Generated Abelian Groups And Similarity Of Matrices Over A Field

Author : Christopher Norman
ISBN : 9781447127291
Genre : Computers
File Size : 66. 45 MB
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This book provides an introduction to the decomposition of finitely generated abelian groups and canonical forms of matrices, and explores the analogous theory of matrix similarity over a field. Includes numerous worked examples and exercises with solutions.

Algebras Rings And Modules

Author : Michiel Hazewinkel
ISBN : 9781402026911
Genre : Mathematics
File Size : 86. 25 MB
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Expository Lectures On Representation Theory

Author : Kiyoshi Igusa
ISBN : 9780821891407
Genre : Mathematics
File Size : 30. 43 MB
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This volume contains the proceedings of the Maurice Auslander Distinguished Lectures and International Conference, held April 25-30, 2012, in Falmouth, MA. The representation theory of finite dimensional algebras and related topics, especially cluster combinatorics, is a very active topic of research. This volume contains papers covering both the history and the latest developments in this topic. In particular, Otto Kerner gives a review of basic theorems and latest results about wild hereditary algebras, Yuri Berest develops the theory of derived representation schemes, and Markus Schmidmeier presents new applications of arc diagrams.

Advanced Modern Algebra Third Edition

Author : Joseph J. Rotman
ISBN : 9781470415549
Genre : Algebra
File Size : 27. 8 MB
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This new edition, now in two parts, has been significantly reorganized and many sections have been rewritten. This first part, designed for a first year of graduate algebra, consists of two courses: Galois theory and Module theory. Topics covered in the first course are classical formulas for solutions of cubic and quartic equations, classical number theory, commutative algebra, groups, and Galois theory. Topics in the second course are Zorn's lemma, canonical forms, inner product spaces, categories and limits, tensor products, projective, injective, and flat modules, multilinear algebra, affine varieties, and Gröbner bases.

Algebraic K Theory And Its Applications

Author : Jonathan Rosenberg
ISBN : 0387942483
Genre : Mathematics
File Size : 22. 65 MB
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Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory.

Fifteen Papers On Algebra

Author :
ISBN : 0821896237
Genre :
File Size : 57. 76 MB
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Author : John Scherk
ISBN : 1584880643
Genre : Mathematics
File Size : 25. 9 MB
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Adequate texts that introduce the concepts of abstract algebra are plentiful. None, however, are more suited to those needing a mathematical background for careers in engineering, computer science, the physical sciences, industry, or finance than Algebra: A Computational Introduction. Along with a unique approach and presentation, the author demonstrates how software can be used as a problem-solving tool for algebra. A variety of factors set this text apart. Its clear exposition, with each chapter building upon the previous ones, provides greater clarity for the reader. The author first introduces permutation groups, then linear groups, before finally tackling abstract groups. He carefully motivates Galois theory by introducing Galois groups as symmetry groups. He includes many computations, both as examples and as exercises. All of this works to better prepare readers for understanding the more abstract concepts. By carefully integrating the use of Mathematica¬ģ throughout the book in examples and exercises, the author helps readers develop a deeper understanding and appreciation of the material. The numerous exercises and examples along with downloads available from the Internet help establish a valuable working knowledge of Mathematica and provide a good reference for complex problems encountered in the field.

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