We define a module M to be G r-extending if for each exact submodule X of M there exists a
direct summand D of M such that X∩ D is essential in both X and D. We investigate G r …

In this article, we define a module M to be G z-extending if and only if for each z-closed
submodule X of M there exists a direct summand D of M such that X∩ D is essential in both …

Let R be a cumulative ring with identity and let M be a unital left R-module. Harada and
Muller introduce the following concept an R-module M is called extending module if every …

An R-module M is called∑-extending if every coproduct of copies of M is extending, ie
closed submodules are direct summands. Oshiro (1984) has shown that the ring R is∑ …

A module M is called extending if every submodule of M is essential in a direct summand.
We call a module FI-extending if every fully invariant submodule is essential in a direct …

Thuyet and Wisbauer considered the extending property for the class of (essentially) finitely
generated submodules. A module M is called ef-extending if every closed submodule which …

A module M is called extending if, for any submodule X of M, there exists a direct summand
of M which contains X as an essential submodule, that is, for any submodule X of M, there …

Modules which are extending relative to module classes Page 1 COMMUNICATIONS IN
ALGEBRA, 26(6), 1699- 172 1 (1998) MODULES WHICH ARE EXTENDING RELATIVE TO …

Rings whose finitely generated modules are extending Page 1 JOURNAL OF PURE AND
Journal of Pure and Applied Algebra 111 (1996) 325-328 APPLIED ALGEBRA Rings whose …

The notion of $\mathcal {K} $-extending modules was defined recently as a proper
generalization of both extending modules and Rickart modules. Let $ M $ be a right $ R …