非可換代数入門（テキスト・第２版） Introduction to Noncommutative Algebra〈Second Edition 2025〉（2）

著者名：Brešar, Matej

Springer（2025/08/29発売）

• 言語：ENG
• ISBN：9783031962950
• eISBN：9783031962967

Description

This textbook offers an elementary introduction to noncommutative rings and algebras. Beginning with the classical theory of finite-dimensional algebras, it then develops a more general structure theory of rings, grounded in modules and tensor products. The final chapters cover free algebras, polynomial identities, and rings of quotients.

Many results are presented in a simplified form rather than in full generality, with an emphasis on clear and understandable exposition. Prerequisites are kept to a minimum, and new concepts are introduced gradually and carefully motivated. Introduction to Noncommutative Algebra is thus accessible to a broad mathematical audience, though it is primarily intended for beginning graduate students and advanced undergraduates encountering the subject for the first time.

This new edition includes several additions and improvements, while preserving the original text’s character and approach.

Praise for the first edition:

“It will soon find its place in classrooms” — Plamen Koshlukov, Mathematical Reviews

“Very well written [...] very pleasant to read” — Veereshwar A. Hiremath, zbMATH

“An excellent choice for a first graduate course” — D. S. Larson, Choice

Table of Contents

Chapter 1. Finite Dimensional Division Algebras.- Chapter 2. Structure of Finite Dimensional Algebras.- Chapter 3. Modules and Semisimple Rings.- Chapter 4. Structure of Rings.- Chapter 5. Tensor Products in Noncommutative Algebra.- Chapter 6. Noncommutative Polynomials.- Chapter 7. Rings of Quotients and Structure of PI-Rings.