In this article we study modules with the condition that every z-closed submodule has a
complement which is a direct summand. This new class of modules properly contains the …

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 …

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 paper, we introduce a new concept named St-polyform modules, and show that the
class of Stpolyform modules is contained properly in the well-known classes; polyform …

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A right module over a ring is called small dual-ADS, if for each decomposition then and are
mutually small projective. Small dual-ADS modules are the dual analogue of LADS …

Beaumont studied groups with isomorphic proper subgroups (see Beaumont: Bull Amer
Math Soc 51, 381–387 1945 1). In Beaumont et al.: Trans Amer Math Soc 91 (2), 209–219 …

Themain aim of this research is to present and study several basic characteristics of the idea
of t-extending semimodules. The semimodule F is said to be a t-extending semimodule if …

We give some conditions as to when a (finite) direct sum of NCS modules (if no non-zero
complement submodule is small) is again NCS, and also provide various conditions to be …

Let R be a commutative ring and M be a unital R-module. The intersection graph of
submodules of M, denoted by GM, is the graph whose vertex set is the collection of all …