Let R be a ring and M a right R-module. We call M, a δ (M)-coretractable module if for every
proper submodule N of M containing δ (M), there is a nonzero homomorphism from M/N to …

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∑ …

After hereditary rings were defined, as a natural generalization, semi-hereditary rings were
introduced. In this article, we study the notion of a finite Σ-Rickart module, as a module …

The study of the endomorphism rings of modules and connections between a module and its
endomorphism ring have long been of interest. Of particular interest has been a quest of …

Let M and X be R-modules. We define the X--supplemented modules via the class  B
(M, X) as a generalization of-supplemented modules. We show that any finite direct sum …

We introduce the notion of I-lifting modules as a proper generalization of the notion of lifting
modules and present some properties of this class of modules. It is shown that if M is an I …

A module $ M $ is called ECS if every ec-closed submodule of $ M $ is a direct summand. It
was shown that the ECS property lies strictly between CS and P-extending properties. We …

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 …

‎ A module $ M $ is called FI-extending if every fully invariant submodule of $ M $ is essential
in a direct summand of $ M $‎.‎ It is not known whether a direct summand of an FI-extending …