
02344677
b
2002b.01415
Lang, Serge
Algebra.
Springer, New York, NY (ISBN 038795385X). 929 p. (2002).
2002
Springer, New York, NY
EN
H15
The book is intended as a basic text for a oneyear course in algebra at the graduate level, or as a useful reference for mathematicians and professionals who use higherlevel algebra. It addresses the basic concepts of algebra. For the revised third edition, the author has included additional exercises and made numerous corrections to the text. Contents: (I) The basic objects of algebra (Groups; Rings; Modules; Polynomials); (II) Algebraic equations (Algebraic extensions; Galois theory; Extensions of rings; Transcendental extensions; Algebraic spaces; Noetherian Rings and Modules; Real fields; Absolute values); (III) Linear algebra and representations (Matrices and linear maps; Representation of one endomorphism; Structure of bilinear forms; The tensor product; Semisimplicity; Representations of finite groups; The alternating product); (IV) Homological algebra (General homology theory; Finite free resolutions); Appendices (The transcendence of e and pi; Some set theory; Bibliography).