ENGLISH

Module theory: an approach to linear algebra

By T. S. Blyth

Book information

Publisher
OUP
Year
1977
ISBN
9780198531623, 0198531621
LCC
QA247 .B57
Open Library ID
OL4539936M
Language
english
Format
DJVU
Filesize
3 MB (2871970 bytes)
Pages
410\410
Topic
Mathematics Algebra
Library
Kolxo3
DPI
600
Scanned
yes
Time added
2010-07-29 05:14:56

Description

The aim of this textbook is to develop the basic properties of modules and to show their importance in the theory of linear algebra. It is intended to provide a self-contained course as well as to indicate how the theory may be developed in a number of more advanced directions. Throughout, numerous exercises will enable readers to consolidate their understanding. Prerequisites are few, being only a familiarity with the basic notions of rings, fields, and groups. The first eleven chapters provide a carefully graded introduction to the central results and applications of the theory of modules. Subsequent chapters deal with advanced linear algebra (including multilinear and tensor algebra) and tackle more advanced topics. These include the exterior product approach to the determinants of matrices, a module-theoretic approach to the structure of finitely generated Abelian groups, canonical forms, and normal transformations. This edition has been revised to accommodate many suggestions to ensure its suitability for undergraduate courses. One advanced topic now covered is a proof of the celebrated Wedderburn-Artin theorem which determines the structure of simple Artinian rings.

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