عنوان

Cyclic modules and the structure of rings /

(Number (ISBN

0191641545

(Number (ISBN

0191746029

(Number (ISBN

128363953X

(Number (ISBN

6613951994

(Number (ISBN

9780191641541

(Number (ISBN

9780191746024

(Number (ISBN

9781283639538

(Number (ISBN

9786613951991

Erroneous ISBN

019966451X

Erroneous ISBN

9780199664511

Number

dltt

Title Proper

Cyclic modules and the structure of rings /

General Material Designation

[Book]

First Statement of Responsibility

by S.K. Jain, Ashish K. Srivastava, Askar A. Tuganbaev

Specific Material Designation and Extent of Item

1 online resource

Series Title

Oxford mathematical monographs

Text of Note

Includes bibliographical references and index

Text of Note

""Cover""; ""Contents""; ""1 Preliminaries""; ""1.1 Artinian and noetherian modules""; ""1.2 Free modules, projective modules, and injective modules""; ""1.3 Hereditary and semihereditary rings""; ""1.4 Generalizations of injectivity""; ""2 Rings characterized by their proper factor rings""; ""2.1 Restricted artinian rings""; ""2.2 Restricted perfect rings""; ""2.3 Restricted von Neumann regular rings""; ""2.4 Restricted self-injective rings""; ""3 Rings each of whose proper cyclic modules has a chain condition""; ""3.1 Rings each of whose proper cyclic modules is artinian""

Text of Note

""10 Rings with cyclics N[sub(0)]-injective, weakly injective, or quasi-projective""""10.1 Rings each of whose cyclic modules is N[sub(0)]-injective""; ""10.2 Rings each of whose cyclic modules is weakly injective""; ""10.3 Rings each of whose cyclic modules is quasi-projective""; ""11 Hypercyclic, q-hypercyclic, and [pi]-hypercyclic rings""; ""11.1 Hypercyclic rings""; ""11.2 q-hypercyclic rings""; ""11.3 [pi]-hypercyclic rings""; ""12 Cyclic modules essentially embeddable in free modules""; ""13 Serial and distributive modules""

Text of Note

""14 Rings characterized by decompositions of their cyclic modules""""15 Rings each of whose modules is a direct sum of cyclic modules""; ""16 Rings each of whose modules is an I[sub(0)]-module""; ""17 Completely integrally closed modules and rings""; ""18 Rings each of whose cyclic modules is completely integrally closed""; ""19 Rings characterized by their one-sided ideals""; ""19.1 Rings each of whose one-sided ideals is quasi-injective""; ""19.2 Rings each of whose one-sided ideals is a direct sum of quasi-injectives""; ""19.3 Rings each of whose one-sided ideals is [pi]-injective""

Text of Note

""3.2 Rings with restricted minimum condition""""3.3 Rings each of whose proper cyclic modules is perfect""; ""4 Rings each of whose cyclic modules is injective (or CS)""; ""4.1 Rings where each cyclic module is injective""; ""4.2 Rings each of whose cyclic modules is CS""; ""5 Rings each of whose proper cyclic modules is injective""; ""6 Rings each of whose simple modules is injective (or [Sigma]-injective)""; ""6.1 V -rings""; ""6.2 WV-rings""; ""6.3 [Sigma]-V rings""; ""6.4 CSI rings""; ""7 Rings each of whose (proper) cyclic modules is quasi-injective""

Text of Note

""7.1 Rings each of whose cyclic modules is quasi-injective""""7.2 Rings each of whose proper cyclic modules is quasi-injective""; ""8 Rings each of whose (proper) cyclic modules is continuous""; ""8.1 Rings each of whose cyclic modules is continuous""; ""8.2 Rings each of whose proper cyclic modules is continuous""; ""9 Rings each of whose (proper) cyclic modules is [pi]-injective""; ""9.1 Rings each of whose cyclic modules is [pi]-injective""; ""9.2 Rings each of whose proper cyclic modules is [pi]-injective""

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Text of Note

This unique and comprehensive volume provides an up-to-date account of the literature on the subject of determining the structure of rings over which cyclic modules or proper cyclic modules have a finiteness condition or a homological property. The finiteness conditions and homological properties are closely interrelated in the sense that either hypothesis induces the other in some form. This is the first book to bring all of this important material on the subject together. Over the last 25 years or more numerous mathematicians have investigated rings whose factor rings or factor modules have a finiteness condition or a homological property. They made important contributions leading to new directions and questions, which are listed at the end of each chapter for the benefit of future researchers. There is a wealth of material on the topic which is combined in this book, it contains more than 200 references and is not claimed to be exhaustive. This book will appeal to graduate students, researchers, and professionals in algebra with a knowledge of basic noncommutative ring theory, as well as module theory and homological algebra, equivalent to a one-year graduate course in the theory of rings and modules

Source for Acquisition/Subscription Address

MIL

Stock Number

395199

Title

Cyclic modules and the structure of rings.

International Standard Book Number

9780199664511

Noncommutative rings

Artin rings

Commutative rings

Noetherian rings

MAT

MAT-- 002040

Number

Edition

Class number

Jain, S. K.

Srivastava, Ashish K.

Tuganbaev, Askar A.

Date of Transaction

20170726092743.0

Cataloguing Rules (Descriptive Conventions))

pn

Electronic name

[Book]

Y