This 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 Ktheory, homological algebra and algebraic number theory.
About A.J. Berrick
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Author  :  A.J. Berrick 
Publisher  :  Cambridge University Press 
Data Published  :  01 May 2000 
ISBN  :  0521632749 
EAN  :  9780521632744 
Format Book  :  PDF, Epub, DOCx, TXT 
Number of Pages  :  282 pages 
Age +  :  15 years 
Language  :  English 
Rating  : 
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