Let R be a ring and℘ be a proper class. In this paper we introduced a new class of R-
modules called℘-supplement submodules and studied its properties, we proved that all …

Let R be a ring and M a right R-module. M is called--δ⊕ supplemented, if every submodule
of M has a-δ supplemented that is a direct summand of M. In this paper, several properties of …

Let R be a ring and M a right R-module. M is called⌖-supplemented if every submodule of M
has a supplement that is a direct summand of M, and M is called completely⌖-supplemented …

Let $ R $ be a commutative ring with identity and let $ M $ be an $ R $-module. A proper
submodule $ N $ of $ M $ is said to be an $ r $-submodule if $ am\in N $ with $(0: _Ma)= 0 …

Let R be a ring and M be a left R− module. We say that an R− module M is a generalized⊕−
δ− supplemented module if every submodule of M has a generalized δ− supplement which …

Let R be a commutative ring with unity and M be an R-module. The aim of this article is to
introduce and investigate certain properties of a new notion of prime submodules of a …

Let $ R $ be a ring and $ M $ be a left $ R $-module. $ M $ is called generalized $\oplus $-
supplemented if every submodule of $ M $ has a generalized supplement that is a direct …

We investigate some properties of n-submodules. More precisely, we find a necessary and
sufficient condition for every proper submodule of a module to be an n-submodule. Also, we …

Let R be a commutative ring and M an R-module. In this paper, we study the dual notion of
prime submodules (that is, second submodules of M) and investigate the conditions under …

Let $ R $ be a commutative ring with identity, $ S $ a multiplicatively closed subset of $ R $,
and $ M $ be an $ R $-module. In this paper, we study and investigate some properties of …