Weakly minimal modules over integral group rings and over related classes of rings

被引：0

作者：

Leonesi, S ^{[1
]}

L'Innocente, S ^{[1
]}

Toffalori, C ^{[1
]}

机构：

[1] Univ Camerino, Dipartimento Matemat & Informat, I-62032 Camerino, Italy

来源：

MATHEMATICAL LOGIC QUARTERLY | 2005年 / 51卷 / 06期

关键词：

weakly minimal module; Prufer domain; group ring; Dedekind-like ring;

D O I：

10.1002/malq.200410053

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A module is weakly minimal if and only if every pp-definable subgroup is either finite or of finite index. We study weakly minimal modules over several classes of rings, including valuation domains, Prufer domains and integral group rings.

引用

页码：613 / 625

页数：13

共 15 条

[1] On pure-injective modules over pullback rings
Atani, SE
[J]. COMMUNICATIONS IN ALGEBRA, 2000, 28 (09) : 4037 - 4069
[2] Curtis C. W., 1962, Representation theory of finite groups and associative algebras, VXI
[3] Curtis C. W., 1981, METHODS REPRESENTATI, VI
[4] Eklof P.C., 1972, ANN MATH LOGIC, V4, P115, DOI [DOI 10.1016/0003-4843(72)90013-7, 10.1016/0003-4843(72)90013-7]
[5] FUCHS L, 1985, MODULES VALUATION DO
[6] FUCHS L, 2001, MODULES NON NOETHERI
[7] MIXED MODULES OVER ZG, G CYCLIC OF PRIME-ORDER, AND OVER RELATED DEDEKIND PULLBACKS
LEVY, LS
[J]. JOURNAL OF ALGEBRA, 1981, 71 (01) : 62 - 114
[8] MODULES OVER DEDEKIND-LIKE RINGS
LEVY, LS
[J]. JOURNAL OF ALGEBRA, 1985, 93 (01) : 1 - 116
[9] LINNOCENTE S, IN PRESS COMM ALGEBR
[10] WEAKLY MINIMAL GROUPS OF UNBOUNDED EXPONENT
LOVEYS, J
[J]. JOURNAL OF SYMBOLIC LOGIC, 1990, 55 (03) : 928 - 937

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