Algebra A Teaching and Source Book /

• Main Authors: Shult, Ernest (Author), Surowski, David (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Subjects: Mathematics.; Algebra.; Associative rings.; Rings (Algebra).; Field theory (Physics).; Group theory.; Associative Rings and Algebras.; Group Theory and Generalizations.; Field Theory and Polynomials.

This book presents a graduate-level course on modern algebra. It can be used as a teaching book – owing to the copious exercises – and as a source book for those who wish to use the major theorems of algebra. The course begins with the basic combinatorial principles of algebra: posets, chain conditi...

Table of Contents:

• Basics
• Basic Combinatorial Principles of Algebra
• Review of Elementary Group Properties
• Permutation Groups and Group Actions
• Normal Structure of Groups
• Generation in Groups
• Elementary Properties of Rings
• Elementary properties of Modules
• The Arithmetic of Integral Domains
• Principal Ideal Domains and Their Modules
• Theory of Fields
• Semiprime Rings
• Tensor Products.