Introduction to Noncommutative Algebra

✍ Scribed by Matej Brešar (auth.)

• Publisher: Springer International Publishing
• Year: 2014
• Tongue: English
• Leaves: 227
• Series: Universitext
• Edition: 1
• Category: Library

✦ Synopsis

Providing an elementary introduction to noncommutative rings and algebras, this textbook begins with the classical theory of finite dimensional algebras. Only after this, modules, vector spaces over division rings, and tensor products are introduced and studied. This is followed by Jacobson's structure theory of rings. The final chapters treat free algebras, polynomial identities, and rings of quotients.

Many of the results are not presented in their full generality. Rather, the emphasis is on clarity of exposition and simplicity of the proofs, with several being different from those in other texts on the subject. Prerequisites are kept to a minimum, and new concepts are introduced gradually and are carefully motivated. Introduction to Noncommutative Algebra is therefore accessible to a wide mathematical audience. It is, however, primarily intended for beginning graduate and advanced undergraduate students encountering noncommutative algebra for the first time.

✦ Table of Contents

Front Matter....Pages i-xxxvii
Finite Dimensional Division Algebras....Pages 1-23
Structure of Finite Dimensional Algebras....Pages 25-51
Modules and Vector Spaces....Pages 53-77
Tensor Products....Pages 79-106
Structure of Rings....Pages 107-136
Noncommutative Polynomials....Pages 137-161
Rings of Quotients and Structure of PI-Rings....Pages 163-191
Back Matter....Pages 193-199

✦ Subjects

Associative Rings and Algebras