Cyclic Modules and the Structure of Rings

Name: Cyclic Modules and the Structure of Rings
Brand: OUP Oxford
Price: 115.59 EUR
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Ashish K. Srivastava Askar A. Tuganbaev S.K. Jain(Autor*in)

OUP Oxford (Verlag)

1. Auflage

Erschienen am 1. September 2012

231 Seiten

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Inhalt

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

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