Basic notions of algebra
Author(s)
Bibliographic Information
Basic notions of algebra
（Encyclopaedia of mathematical sciences / editor-in-chief, R.V. Gamkrelidze, v. 11 . Algebra ; 1）
Springer, c2005
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Itogi nauki i tekhniki, Sovremennye problemy matematiki
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Note
"Originally published as Algebra I by A.I. Kostrikin and I.R. Shafarevich (eds.), volume 11 of the Encyclopaedia of mathematical sciences"--T.p. verso
Includes bibliographical references (p. 244-248) and indexes
Description and Table of Contents
Description
Wholeheartedly recommended to every student and user of mathematics, this is an extremely original and highly informative essay on algebra and its place in modern mathematics and science. From the fields studied in every university maths course, through Lie groups to cohomology and category theory, the author shows how the origins of each concept can be related to attempts to model phenomena in physics or in other branches of mathematics. Required reading for mathematicians, from beginners to experts.
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.- K-theory.
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