Basic Algebra Along with a companion volume Advanced Algebra /

• Main Author: Knapp, Anthony W. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2006.
• Series: Cornerstones,
• Subjects: Mathematics.; Algebra.; Associative rings.; Rings (Algebra).; Commutative algebra.; Commutative rings.; Field theory (Physics).; Group theory.; Matrix theory.; Linear and Multilinear Algebras, Matrix Theory.; Associative Rings and Algebras.; Group Theory and Generalizations.; Field Theory and Polynomials.; Commutative Rings and Algebras.

Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole. Key topics and fea...

Table of Contents:

• Preliminaries about the Integers, Polynomials, and Matrices
• Vector Spaces over ?, ?, and ?
• Inner-Product Spaces
• Groups and Group Actions
• Theory of a Single Linear Transformation
• Multilinear Algebra
• Advanced Group Theory
• Commutative Rings and Their Modules
• Fields and Galois Theory
• Modules over Noncommutative Rings.