Introduction to rings and modules: with K-theory in view

By:

Berrick, A. J

Contributor(s):

Keating, M. E

Material type: Book

BookSeries: Cambridge studies in advanced mathematics 65Publication details: Cambridge: Cambridge University Press, 2000.Description: xv, 265 p. ; hb. ; 23 cmISBN:

9780521632744

Subject(s):

DDC classification:

512.4 BER

Summary: This book, first published in 2000, is a concise introduction to ring theory, module theory and number theory, ideal for a first year graduate student, as well as an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences. It then explores the structure of modules over various types of ring: noncommutative polynomial rings, Artinian rings (both semisimple and not), and Dedekind domains. It also shows how Dedekind domains arise in number theory, and explicitly calculates some rings of integers and their class groups. About 200 exercises complement the text and introduce further topics. This book provides the background material for the authors' companion volume Categories and Modules, soon to appear. Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory.

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Holdings
Item type	Current library	Collection	Call number	Copy number	Status	Date due	Barcode
Books	IIT Gandhinagar General Stacks	General	512.4 BER (Browse shelf(Opens below))	1	Available		030055

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Previous	512.32 SZA Galois groups and fundamental groups	512.33 GRI Topics in transcendental algebraic geometry	512.4 AUS Representation theory of Artin algebras	512.4 BER Introduction to rings and modules: with K-theory in view	512.4 KNO Infinite sequences and series	512.4 WIN Cohen-Macaulay rings	512.42 LAU Cohomology of drinfeld modular varieties: part 1. geometry, counting of points and local harmonic analysis	Next

The book contains refrences and index.

This book, first published in 2000, is a concise introduction to ring theory, module theory and number theory, ideal for a first year graduate student, as well as an excellent reference for working mathematicians in other areas. Starting from definitions, the book introduces fundamental constructions of rings and modules, as direct sums or products, and by exact sequences. It then explores the structure of modules over various types of ring: noncommutative polynomial rings, Artinian rings (both semisimple and not), and Dedekind domains. It also shows how Dedekind domains arise in number theory, and explicitly calculates some rings of integers and their class groups. About 200 exercises complement the text and introduce further topics. This book provides the background material for the authors' companion volume Categories and Modules, soon to appear. Armed with these two texts, the reader will be ready for more advanced topics in K-theory, homological algebra and algebraic number theory.

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