Brešar / Bresar Introduction to Noncommutative Algebra

2. Auflage 2025
ISBN: 978-3-031-96296-7
Verlag: Springer International Publishing
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 234 Seiten

Reihe: Mathematics and Statistics

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. 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:

“” — Plamen Koshlukov, Mathematical Reviews

“ [...] ” — Veereshwar A. Hiremath, zbMATH

“” — D. S. Larson, Choice

Zielgruppe

Graduate

Autoren/Hrsg.

Brešar, Matej

Bresar, Matej

Inhaltsverzeichnis

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.

Über Autor(innen)

Matej Brešar is a Professor of Mathematics at University of Ljubljana and University of Maribor. His research focus lies in noncommutative algebra and its applications. He is the author or co-author of over 175 research papers as well as four books published by Springer Nature.