In this paper, we study mod-retractable modules, CSL-modules, fully Kasch modules, and
their interrelations. Right fully Kasch rings are described. It is proved that for a module M of …

Let $ R $ be a ring and $ M $ a right $ R $-module. We call $ M $, coretractable relative to
$\overline {Z}(M) $(for short, $\overline {Z}(M) $-coretractable) provided that, for every proper …

The modules which are isomorphic to their non-zero submodules are known as iso-
retractable. We characterize simple modules in terms of iso-retractable modules. We provide …

An R-module M is called coretractable if HomR (M/K, M)≠ 0 for any proper submodule K of
M. In this paper we study coretractable modules and their endomorphism rings. It turns out …

Extension closure of relative syzygy modules Page 1 Vol. 46 No. 5 SCIENCE IN CHINA (Series
A) September 2003 Extension closure of relative syzygy modules HUANG Zhaoyong ( ¢¡) …

Full article: Extension Closure of Relative k-Torsionfree Modules Skip to Main Content Taylor and
Francis Online homepage Taylor and Francis Online homepage Access provided by The …

An associative ring R is a left Kasch ring if it contains a copy of every simple left R-module.
Transferring this notion to modules we call a left R-module M a Kasch module if it contains a …

We carry out a study of modules MR satisfying the property that every module in σ [M] is a
Kasch module. Such modules are called fully Kasch. Several sufficient conditions for a …

A module RM is said to be retractable if HomR (M, U)≠ 0 for each nonzero submodule U of
M. M is said to be a CS module if every complement submodule of M is a direct summand in …

Let R be a commutative noetherian ring. Denote by mod\, R mod R the category of finitely
generated R-modules. In this paper, we study n-torsionfree modules in the sense of …