Martin Mathieu: Classically Semisimple Rings

Cover: 9783031142086 | Classically Semisimple Rings | Martin Mathieu | Taschenbuch | xvi

Rückseite: 9783031142086 | Classically Semisimple Rings | Martin Mathieu | Taschenbuch | xvi

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Sprache: Englisch

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Beschreibung

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 Wedderburn¿Artin 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, Rickart¿s 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.

Classically Semisimple Rings is a textbook on rings, modules and categories, aimed at advanced undergraduate and beginning graduate students.

Über den Autor

Martin Mathieu is Professor of Pure Mathematics at Queen's University Belfast. He received his Dr. [...] and his Habilitation from the University of Tübingen, where he was Privatdozent until 1998. After various spells at the University of the Saarland, Saarbrücken; the University of Iowa, Iowa City; and NUI Maynooth, Maynooth he moved to Northern Ireland where he has been living with his family since.

Zusammenfassung

Provides a clear yet concise first course on semisimple rings and modules

Uses category theory to cast a classical theory in a modern setting

Introduces readers to original topics such as exchange rings and the semiprimitivity of group rings

Inhaltsverzeichnis

Introduction.- Chapter 1. Motivation from Ring Theory.- Chapter 2. Constructions with Modules.- Chapter 3. The Isomorphism Theorems.- Chapter 4. Noetherian Modules.- Chapter 5. Artinian Modules.- Chapter 6. Simple and Semisimple Modules.- Chapter 7. The Artin-Weddeburn Theorem.- Chapter 8. Tensor Products of Modules.- Chapter 9. Exchange Modules and Exchange Rings.- Chapter 10. Semiprimitivity of Group Rings.- Bibliography.- Index of Symbols.- Index.

Details

Erscheinungsjahr:	2022
Fachbereich:	Allgemeines
Genre:	Mathematik , Medizin , Naturwissenschaften , Technik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xvi 151 S. 37 s/w Illustr. 151 p. 37 illus.
ISBN-13:	9783031142086
ISBN-10:	303114208X
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Mathieu, Martin
Auflage:	1st edition 2022
Hersteller:	Springer Nature Switzerland Springer International Publishing
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 10 mm
Von/Mit:	Martin Mathieu
Erscheinungsdatum:	20.12.2022
Gewicht:	0,265 kg