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Modules and the structure of rings : a primer / by Golan.
Author
Golan
[Browse]
Format
Book
Language
English
Εdition
First edition.
Published/Created
Boca Raton, FL : CRC Press, an imprint of Routledge, [2017].
©1991
Description
1 online resource (288 pages) : illustrations.
Availability
Available Online
SCI-TECHnetBASE
Taylor & Francis eBooks Complete
Details
Subject(s)
Modules (Algebra)
[Browse]
Rings (Algebra)
[Browse]
Related name
CRC Press
[Browse]
Series
Monographs and textbooks in pure and applied mathematics ; 147.
[More in this series]
Pure and Applied Mathematics
Monographs and Textbooks in Pure and Applied Mathematics ; 147
Summary note
This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs. avoids the formalism of category theory. aids independent study or seminarwork. and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.
Bibliographic references
Includes bibliographical references and index.
Source of description
Description based on print version record.
Contents
part 1 Fundamental Concepts / Jonathan S. Golan
chapter Modules and Maps / Jonathan S. Golan
chapter The Ring as a Module over Itself / Jonathan S. Golan
part 1 Projectivity / Jonathan S. Golan
chapter Coproducts of Copies of R (Free Modules) / Jonathan S. Golan
chapter Direct Summands of Free Modules (Projective Modules) / Jonathan S. Golan
chapter Submodules of Free Modules / Jonathan S. Golan
chapter Factor Modules of Free Modules / Jonathan S. Golan
part 2 Injectivity / Jonathan S. Golan
chapter Enlarging Homomorphisms / Jonathan S. Golan
chapter Embedding Modules in Injective Modules / Jonathan S. Golan
chapter Injective Modules as a Class / Jonathan S. Golan
chapter Structure of Injective Modules / Jonathan S. Golan
part 3 Countability / Jonathan S. Golan
chapter Finitely-Generated Modules / Jonathan S. Golan
chapter Countably-Generated Modules / Jonathan S. Golan
chapter Coproducts of Countably-Generated Modules / Jonathan S. Golan
chapter Projective Modules / Jonathan S. Golan
part 4 Part Four Rings and Modules of Quotients / Jonathan S. Golan
chapter Torsion and Torsion free Modules / Jonathan S. Golan
chapter The Module of Quotients / Jonathan S. Golan
chapter Rings of Quotients / Jonathan S. Golan.
Show 19 more Contents items
ISBN
1-351-43037-8
0-203-74661-9
1-351-43036-X
OCLC
1028858304
Doi
10.1201/9780203746615
Statement on language in description
Princeton University Library aims to describe library materials in a manner that is respectful to the individuals and communities who create, use, and are represented in the collections we manage.
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Other versions
Modules and the structure of rings : a primer / Jonathan S. Golan, Tom Head.
id
996536483506421
Modules and the structure of rings : a primer / Jonathan S. Golan, Tom Head.
id
99124265153506421