Rings and Their Modules

1. Auflage 2011
ISBN: 978-3-11-025022-0
Verlag: De Gruyter

Buch, Englisch, 452 Seiten, Format (B × H): 170 mm x 240 mm, Gewicht: 785 g

Reihe: De Gruyter Textbook

This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. The theme of the text is the interplay between rings and modules. At times rings are investigated by considering given sets of conditions on the modules they admit and at other times rings of a certain type are considered to see what structure is forced on their modules. Standard topics in ring and module theory such as chain conditions on rings and modules, injective and projective modules and semisimple rings are included as well as subjects like category theory and homological algebra. The text also contains presentations on topics such as flat modules and coherent rings, injective envelopes, projective covers and perfect rings, reflexive modules and quasi-Frobenius rings, and graded rings and modules. The book is a self-contained volume written in a very systematic style: all proofs are clear and easy for the reader to understand and all arguments are based on materials contained in the book. A problem sets follow each section. It is assumed that the reader is familiar with concepts such as Zorn's lemma, commutative diagrams and ordinal and cardinal numbers. It is also assumed that the reader has a basic knowledge of rings and their homomorphisms. The text is suitable for graduate and PhD students who have chosen ring theory for their research subject.

Zielgruppe

Students, Researchers, Academic Libraries

Autoren/Hrsg.

Bland, Paul E.

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

Frontmatter

Preface

Contents

0 Preliminaries

1 Basic Properties of Rings and Modules

2 Fundamental Constructions

3 Categories

4 Chain Conditions

5 Injective, Projective, and Flat Modules

6 Classical Ring Theory

7 Envelopes and Covers

8 Rings and Modules of Quotients

9 Graded Rings and Modules

10 More on Rings and Modules

11 Introduction to Homological Algebra

12 Homological Methods

A Ordinal and Cardinal Numbers

Bibliography

List of Symbols

Index

Über Autor(innen)

Bland, Paul E.
Paul E. Bland, Eastern Kentucky University, USA.