Cyclic Modules and the Structure of Rings
1st Edition
Published on 1. September 2012
231 pages
978-0-19-164154-1 (ISBN)
Description
This unique 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.
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S.K. Jain | Ashish K. Srivastava | Askar A. Tuganbaev
Cyclic Modules and the Structure of Rings
Book
09/2012
Oxford University Press
€195.10
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Content
- 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 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 S-injective)
- 6.1 V -rings
- 6.2 WV-rings
- 6.3 S-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 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 p-injective
- 9.1 Rings each of whose cyclic modules is p-injective
- 9.2 Rings each of whose proper cyclic modules is p-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-projective
- 11 Hypercyclic, q-hypercyclic, and p-hypercyclic rings
- 11.1 Hypercyclic rings
- 11.2 q-hypercyclic rings
- 11.3 p-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 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 p-injective
- 19.4 Rings each of whose one-sided ideals is a direct sum of p-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
