Algebra An Approach Via Module Theory

Name: Algebra An Approach Via Module Theory
Price: 58.2 USD
Availability: InStock
ISBN: 9780387978390

ISBN-10: 0387978399

ISBN-13: 9780387978390

Edition: 1992

Authors: William A. Adkins, Steven H. Weintraub, J. H. Ewing, F. W. Gehring, P. R. Halmos

List price: $79.95

30 day, 100% satisfaction guarantee!

Marketplace

2 new & used from $58.20

what's this?

Rush Rewards U
Members Receive:

You have reached 400 XP and carrot coins. That is the daily max!

Description:

This book is designed as a text for a first-year graduate algebra course. The choice of topics is guided by the underlying theme of modules as a basic unifying concept in mathematics. Beginning with standard topics in groups and ring theory, the authors then develop basic module theory, culminating in the fundamental structure theorem for finitely generated modules over a principal ideal domain. They then treat canonical form theory in linear algebra as an application of this fundamental theorem. Module theory is also used in investigating bilinear, sesquilinear, and quadratic forms. The authors develop some multilinear algebra (Hom and tensor product) and the theory of semisimple rings and…

Book details

List price: $79.95
Copyright year: 1992
Publisher: Springer
Publication date: 4/23/1999
Binding: Hardcover
Pages: 526
Size: 6.75" wide x 9.75" long x 1.25" tall
Weight: 1.980
Language: English



Preface



Groups



Definitions and Examples



Subgroups and Cosets



Normal Subgroups, Isomorphism Theorems, and Automorphism Groups



Permutation Representations and the Sylow Theorems



The Symmetric Group and Symmetry Groups



Direct and Semidirect Products



Groups of Low Order



Exercises



Rings



Definitions and Examples



Ideals, Quotient Rings, and Isomorphism Theorems



Quotient Fields and Localization



Polynomial Rings



Principal Ideal Domains and Euclidean Domains



Unique Factorization Domains



Exercises



Modules and Vector Spaces



Definitions and Examples



Submodules and Quotient Modules



Direct Sums, Exact Sequences, and Hom



Free Modules



Projective Modules



Free Modules over a PID



Finitely Generated Modules over PIDs



Complemented Submodules



Exercises



Linear Algebra



Matrix Algebra



Determinants and Linear Equations



Matrix Representation of Homomorphisms



Canonical Form Theory



Computational Examples



Inner Product Spaces and Normal Linear Transformations



Exercises



Matrices over PIDs



Equivalence and Similarity



Hermite Normal Form



Smith Normal Form



Computational Examples



A Rank Criterion for Similarity



Exercises



Bilinear and Quadratic Forms



Duality



Bilinear and Sesquilinear Forms



Quadratic Forms



Exercises



Topics in Module Theory



Simple and Semisimple Rings and Modules



Multilinear Algebra



Exercises



Group Representations



Examples and General Results



Representations of Abelian Groups



Decomposition of the Regular Representation



Characters



Induced Representations



Permutation Representations



Concluding Remarks



Exercises


Appendix


Bibliography


Index of Notation


Index of Terminology