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Introduction to ring and module theory

Record Type:	Electronic resources : Monograph/item
Title/Author:	Introduction to ring and module theoryby Alberto Facchini.
Author:	Facchini, Alberto.
Published:	Cham :Springer Nature Switzerland :2025.
Description:	viii, 221 p. :ill., digital ;24 cm.
Contained By:	Springer Nature eBook
Subject:	Rings (Algebra)
Online resource:	https://doi.org/10.1007/978-3-031-82509-5
ISBN:	9783031825095$q(electronic bk.)

Introduction to ring and module theory
Facchini, Alberto.

Introduction to ring and module theory[electronic resource] /by Alberto Facchini. - Cham :Springer Nature Switzerland :2025. - viii, 221 p. :ill., digital ;24 cm. - Compact textbooks in mathematics,2296-455X. - Compact textbooks in mathematics..

- 1. Basic Notions -- 2. Some Classes of Modules -- 3. Right Artinian Rings -- 4. Local Rings, Injective Modules, Flat Modules -- 5. Additive Categories, Abelian Categories -- 6. Appendices.

This textbook is designed for a first course in ring theory, module theory and category theory. Written following several decades of teaching experience, it stands out with its clear and engaging style, featuring thorough explanations and attention to detail. Carefully selected exercises encourage active learning and problem-solving. The textbook integrates elementary category theory with basic concepts and examples developed throughout the course. Although the primary focus is on rings and modules, relevant notions for other algebraic structures, such as groups and semigroups, are also discussed. Thus, this book aims at introducing students to noncommutative rings and modules within a broader algebraic context. Aimed at advanced undergraduates or master students in mathematics, this textbook is suitable both for use in the classroom and self-study. Whereas the first part of the book covers a basic course in ring and module theory, the latter part includes optional deepening topics.

ISBN: 9783031825095$q(electronic bk.)

Standard No.: 10.1007/978-3-031-82509-5doiSubjects--Topical Terms:

190979
Rings (Algebra)

LC Class. No.: QA247

Dewey Class. No.: 512.4

Introduction to ring and module theory
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505 0 $a - 1. Basic Notions -- 2. Some Classes of Modules -- 3. Right Artinian Rings -- 4. Local Rings, Injective Modules, Flat Modules -- 5. Additive Categories, Abelian Categories -- 6. Appendices.
520 $a This textbook is designed for a first course in ring theory, module theory and category theory. Written following several decades of teaching experience, it stands out with its clear and engaging style, featuring thorough explanations and attention to detail. Carefully selected exercises encourage active learning and problem-solving. The textbook integrates elementary category theory with basic concepts and examples developed throughout the course. Although the primary focus is on rings and modules, relevant notions for other algebraic structures, such as groups and semigroups, are also discussed. Thus, this book aims at introducing students to noncommutative rings and modules within a broader algebraic context. Aimed at advanced undergraduates or master students in mathematics, this textbook is suitable both for use in the classroom and self-study. Whereas the first part of the book covers a basic course in ring and module theory, the latter part includes optional deepening topics.
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