Basic notions of algebra /

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

Description
Summary:	§22. K-theory 230 A. Topological X-theory 230 Vector bundles and the functor Vec(X). Periodicity and the functors KJX). K(X) and t the infinite-dimensional linear group. The symbol of an elliptic differential operator. The index theorem. B. Algebraic K-theory 234 The group of classes of projective modules. K , K and K of a ring. K of a field and o l n 2 its relations with the Brauer group. K-theory and arithmetic. Comments on the Literature 239 References 244 Index of Names 249 Subject Index 251 Preface This book aims to present a general survey of algebra, of its basic notions and main branches. Now what language should we choose for this? In reply to the question 'What does mathematics study?', it is hardly acceptable to answer 'structures' or 'sets with specified relations'; for among the myriad conceivable structures or sets with specified relations, only a very small discrete subset is of real interest to mathematicians, and the whole point of the question is to understand the special value of this infinitesimal fraction dotted among the amorphous masses. In the same way, the meaning of a mathematical notion is by no means confined to its formal definition; in fact, it may be rather better expressed by a (generally fairly small) sample of the basic examples, which serve the mathematician as the motivation and the substantive definition, and at the same time as the real meaning of the notion.
Item Description:	English ed. originally published in 1990 as: Algebra I.
Physical Description:	1 online resource (258 p.) : ill.
Bibliography:	Includes bibliographical references (p. 244-248) and indexes.
ISBN:	9783540264743 3540264744
ISSN:	0938-0396 ;