Basic notions of algebra /

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Bibliographic Details
Author / Creator:	Shafarevich, I. R. (Igorʹ Rostislavovich), 1923-
Imprint:	Berlin ; New York : Springer, c2005.
Description:	1 online resource (258 p.) : ill.
Language:	English
Series:	Encyclopaedia of mathematical sciences, 0938-0396 ; v. 11 Encyclopaedia of mathematical sciences ; v. 11.
Subject:	Algebra. Algebra.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/8875529

Hidden Bibliographic Details
Other title:	Algebra 1.
Other uniform titles:	Shafarevich, I. R. (Igorʹ Rostislavovich), 1923- Algebra 1.
ISBN:	9783540264743 3540264744
Notes:	English ed. originally published in 1990 as: Algebra I. Includes bibliographical references (p. 244-248) and indexes. Description based on print version record.
Summary:	This book is wholeheartedly recommended to every student or user of mathematics. Although the author modestly describes his book as 'merely an attempt to talk about' algebra, he succeeds in writing an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields, commutative rings and groups studied in every university math course, through Lie groups and algebras to cohomology and category theory, the author shows how the origins of each algebraic concept can be related to attempts to model phenomena in physics or in other branches.
Other form:	Print version: Shafarevich, I.R. (Igorʹ Rostislavovich), 1923- Basic notions of algebra. Berlin ; New York : Springer, c2005 3540251774 9783540251774

Table of Contents:

What is Algebra?; Fields; Commutative Rings; Homomorphisms and Ideals; Modules; Algebraic Aspects of Dimension; The Algebraic View of Infinitesimal Notions; Noncommutative Rings; Modules over Noncommutative Rings; Semisimple Modules and Rings; Division Algebras of Finite Rank; The Notion of a Group; Examples of Groups: Finite Groups; Examples of Groups: Infinite Discrete Groups; Examples of Groups: Lie Groups and Algebraic Groups; General Results of Group Theory; Group Representations; Some Applications of Groups; Lie Algebras and Nonassociative Algebra; Categories; Homological Algebra.

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