Classically semisimple rings : a perspective through modules and categories / Martin Mathieu.

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Classically semisimple rings : a perspective through modules and categories / Martin Mathieu.

9783031142093 electronic book
3031142098 electronic book
303114208X
9783031142086

Cham, Switzerland : Springer, 2022.

English

1 online resource (1 volume) : illustrations (black and white).

10.1007/978-3-031-14209-3 doi

QA251.5 .M38 2022

512/.46

Classically Semisimple Rings is a textbook on rings, modules and categories, aimed at advanced undergraduate and beginning graduate students. The book presents the classical theory of semisimple rings from a modern, category-theoretic point of view. Examples from algebra are used to motivate the abstract language of category theory, which then provides a framework for the study of rings and modules, culminating in the WedderburnArtin classification of semisimple rings. In the last part of the book, readers are gently introduced to related topics such as tensor products, exchange modules and C*-algebras. As a final flourish, Rickarts theorem on group rings ties a number of these topics together. Each chapter ends with a selection of exercises of varying difficulty, and readers interested in the history of mathematics will find biographical sketches of important figures scattered throughout the text. Assuming previous knowledge in linear and basic abstract algebra, this book can serve as a textbook for a course in algebra, providing students with valuable early exposure to category theory.

Includes bibliographical references (pages 145-146) and index.

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