Certain chain conditions in modules over dedekind domains and related rings

被引：1

作者：

Campos, Esperanza Sanchez ^{[1
]}

Smith, Patrick F. ^{[2
]}

机构：

[1] Univ Malaga, Dept Algebra Geometria & Topol, Malaga 29080, Spain

[2] Univ Glasgow, Dept Math, Glasgow G12 8QW, Lanark, Scotland

来源：

MODULES AND COMODULES | 2008年

关键词：

chain conditions; dedekind domain; uniform dimension;

D O I：

10.1007/978-3-7643-8742-6_8

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Necessary and sufficient conditions are given for a module over a Dedekind domain to satisfy the ascending chain condition on n-generated submodules for every positive integer n or on submodules with uniform dimension at most n for every positive integer n. These results are then extended to modules over commutative Noetherian domains which need not be Dedekind.

引用

页码：125 / +

页数：3

共 20 条

[1]

ANTUNES ME, 1998, J PURE APPL ALGEBRA, V123, P51

[2]

ANTUNES ME, 1996, COMMUN ALGEBRA, V24, P1713

[3]

ANTUNES ME, 1995, COMMUN ALGEBRA, V23, P3525

[4]

BAUMSLAG B, 1971, P LOND MATH SOC, V22, P681

[5]

Cohn P.M., 1971, Free rings and their relations

[6]

COHN PM, 1991, ALGEBRAIC NUMBERS AL

[7]

DUNG N. V., 1994, EXTENDING MODULES

[8] Modules with n-acc and the acc on certain types of annihilators [J].

Frohn, D .

JOURNAL OF ALGEBRA, 2002, 256 (02) :467-483

[9] A counterexample concerning ACCP in power series rings [J].

Frohn, D .

COMMUNICATIONS IN ALGEBRA, 2002, 30 (06) :2961-2966

[10]

Fuchs L., 1973, Infinite Abelian Groups, V2

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