Author 
Shafarevich, I. R. (Igorʹ Rostislavovich), 19232017.

Series 
Encyclopaedia of mathematical sciences, 09380396 ; v. 11 

Encyclopaedia of mathematical sciences ;
v. 11.
09380396

Subject 
Algebra.

Alt Name 
Shafarevich, I. R. (Igorʹ Rostislavovich), 19232017.
Algebra 1.

Alternate Title 
Algebra 1.

Description 
1 online resource (258 pages) : illustrations. 

polychrome rdacc 
Bibliography Note 
Includes bibliographical references (pages 244248)and indexes. 
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. 
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. 
Note 
English. 

Print version record. 
ISBN 
9783540264743 

3540264744 

3540251774 

9783540251774 

9783540612216 

3540612211 
ISBN/ISSN 
10.1007/b137643 
OCLC # 
209869067 
Link 
Springer ebooks 
Additional Format 
Print version: Shafarevich, I.R. (Igor Rostislavovich), 1923 Basic notions of algebra. Berlin ; New York : Springer, 2005 3540251774 9783540251774 (OCoLC)61164882 
