Classically Semisimple Rings: A Perspective Through Modules and Categories

Classically Semisimple Rings is a textbook that presents the classical theory of semisimple rings from a modern,category-theoretic point of view,using examples from algebra to motivate abstract language. It covers topics such as tensor products,exchange modules,and C*-algebras,and ends with Rickarts theorem on group rings.

Format: Paperback / softback
Length: 151 pages
Publication date: 20 December 2022
Publisher: Springer International Publishing AG

Classically Semisimple Rings is a comprehensive textbook that delves into the realms of rings, modules, and categories, catering to advanced undergraduate and beginning graduate students. This text presents the classical theory of semisimple rings from a modern, category-theoretic perspective, utilizing examples from algebra to elucidate the abstract language of category theory. This framework serves as a foundation for studying rings and modules, culminating in the Wedderburn–Artin classification of semisimple rings. In the final chapters, readers are introduced to related topics such as tensor products, exchange modules, and C*-algebras, all of which are interconnected by Rickarts theorem on group rings. Each chapter concludes with a range of exercises designed to challenge and engage readers, while those with an interest in the history of mathematics will discover biographical sketches of significant figures interspersed throughout the text. This book assumes a prior understanding of linear and basic abstract algebra and serves as an excellent textbook for a course in algebra, offering students a valuable early exposure to category theory.

Weight: 267g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031142086
Edition number: 1st ed. 2022