Screen LibraryRings and their modules /
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. In addition to the presentation of standard topics in ring and module theory, it also covers category theory, homological algebra and even more special...
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| Main Authors: | |
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| Corporate Authors: | |
| Published: |
De Gruyter,
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| Publisher Address: | Berlin ;Boston : |
| Publication Dates: |
[2011] ©2011 |
| Literature type: | eBook |
| Language: | English |
| Series: |
De gruyter textbook
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| Subjects: | |
| Online Access: |
http://www.degruyter.com/doi/book/10.1515/9783110250237 http://www.degruyter.com/doc/cover/9783110250237.jpg |
| Summary: |
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. In addition to the presentation of standard topics in ring and module theory, it also covers category theory, homological algebra and even more specialized topics like injective envelopes and projective covers, 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 suitable for graduate and PhD students who have chosen ring theory for their research subject. |
| Carrier Form: | 1 online resource (465pages). |
| ISBN: | 9783110250237 |
| Index Number: | QA247 |
| CLC: | O153.3 |
| Contents: |
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 |