Cyclic modules and the structure of rings / S.K. Jain, Ashish K. Srivastava, Askar A. Tuganbaev.

Format:

Book

Author/Creator:

Jain, S. K.

Contributor:

Srivastava, Ashish K.

Tuganbaev, Askar A.

Series:

Oxford Mathematical Monographs

Oxford mathematical monographs

Language:

English

Subjects (All):

Commutative rings.

Noetherian rings.

Artin rings.

Physical Description:

1 online resource (231 p.)

Edition:

1st ed.

Place of Publication:

Oxford : Oxford University Press, 2012.

Language Note:

English

Summary:

This monograph brings together important material in the field of noncommutative rings and modules. It provides an up-to-date account of the topic of cyclic modules and the structure of rings which will be of particular interest to those working in abstract algebra and to graduate students who are exploring potential research topics.

Contents:

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; 3.2 Rings with restricted minimum condition

3.3 Rings each of whose proper cyclic modules is perfect4 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; 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 continuous8.1 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; 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-projective11 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; 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 ideals19.1 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; 19.4 Rings each of whose one-sided ideals is a direct sum of [pi]-injective right ideals; 19.5 Rings each of whose one-sided ideals is weakly injective; 19.6 Rings each of whose one-sided ideals is quasi-projective; References; Index; A; B; C; D; E; F; G; H; I; J; K; L; M; N; P; Q; R; S; U; V; W

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on online resource; title from PDF title page (viewed on Oct. 31, 2012).

Description based on publisher supplied metadata and other sources.

ISBN:

1-283-63953-X

0-19-164154-5

OCLC:

922971331