Эта публикация цитируется в
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RESEARCH ARTICLE
A generalization of supplemented modules
Hatice Inankila,
Sait Halıcıoglub,
Abdullah Harmancic a Department of Mathematics, Gebze Institute of Technology, Kocaeli, Turkey
b Department of Mathematics, Ankara University, Ankara, Turkey
c Department of Maths, Hacettepe University, Ankara, Turkey
Аннотация:
Let
$R$ be an arbitrary ring with identity and
$M$ a right
$R$-module. In this paper, we introduce a class of
modules which is an analogous of
$\delta$-supplemented modules defined by Kosan. The module
$M$ is called
principally $\delta$-supplemented, for all
$m\in M$ there exists a submodule
$A$ of
$M$ with
$M = mR + A$ and
$(mR)\cap A$ $\delta$-small in
$A$. We prove that some results of
$\delta$-supplemented modules can be extended to principally
$\delta$-supplemented modules for this general settings. We supply some examples showing that there are principally
$\delta$-supplemented modules but not
$\delta$-supplemented. We also introduce principally
$\delta$-semiperfect modules as a generalization of
$\delta$-semiperfect modules and investigate their properties.
Ключевые слова:
supplemented modules,
$\delta$-supplemented modules, principally
$\delta$-supplemented modules, semiperfect modules,
$\delta$-semiperfect modules, principally
$\delta$-semiperfect modules.
MSC: 16U80 Поступила в редакцию: 14.03.2011
Исправленный вариант: 14.03.2011
Язык публикации: английский