GOLDIE EXTENDING MODULES

被引：32

作者：

Akalan, Evrim ^{[2
]}

Birkenmeier, Gary F. ^{[1
]}

Tercan, Adnan ^{[2
]}

机构：

[1] Univ Louisiana, Dept Math, Lafayette, LA 70504 USA

[2] Hacettepe Univ, Dept Math, Ankara, Turkey

来源：

COMMUNICATIONS IN ALGEBRA | 2009年 / 37卷 / 02期

关键词：

C-11-module; C-11-ring; Extending module; FI-extending module; Rational hull; Uniform module; SUBMODULE;

D O I：

10.1080/00927870802254843

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this article, we de. ne a module M to be G-extending if and only if for each X <= M there exists a direct summand D of M such that X boolean AND D is essential in both X and D. We consider the decomposition theory for G-extending modules and give a characterization of the Abelian groups which are G-extending. In contrast to the characterization of extending Abelian groups, we obtain that all finitely generated Abelian groups are G-extending. We prove that a minimal cogenerator for Mod-R is G-extending, but not, in general, extending. It is also shown that if M is (G-) extending, then so is its rational hull. Examples are provided to illustrate and delimit the theory.

引用

页码：663 / 683

页数：21

共 20 条

[1]

Abulkheir H. E., 1996, KYUNGPOOK MATH J, V36, P129

[2] When some complement of a submodule is a summand [J].

Birkenmeier, Gary F. ;

Tercan, Adnan .

COMMUNICATIONS IN ALGEBRA, 2007, 35 (02) :597-611

[3] Modules in which every fully invariant submodule is essential in a direct summand [J].

Birkenmeier, GF ;

Müller, BJ ;

Rizvi, ST .

COMMUNICATIONS IN ALGEBRA, 2002, 30 (03) :1395-1415

[4]

Dung N. V., 1994, PITMAN RES NOTES MAT, V313

[5]

Fuchs L., 1970, INFINITE ABELIAN GRO, V1

[6]

Fuchs L., 1973, Infinite Abelian Groups, VII

[7]

Goldie A.W., 1960, Proc. Lond. Math. Soc., V10, P201

[8]

GOODEARL K.R., 1976, RING THEORY NONSINGU

[9]

KAMAL MA, 1988, OSAKA J MATH, V25, P531

[10]

KAMAL MA, 1988, OSAKA J MATH, V25, P539

← 1 2 →