Let M be a left R-module and F a submodule of M for any ring R. We call MF-semiregular if
for every x∈ M, there exists a decomposition M= A⊕ B such that A is projective, A≤ Rx and …

A module M is⊕‐supplemented if every submodule of M has a supplement which is a direct
summand of M. In this paper, we show that a quotient of a⊕‐supplemented module is not in …

A module is regular if all its submodules are (Cohn) pure. The family of all regular modules
is closed under products if and only if R∕ J (R) is a von Neumann regular ring. If each …

The notion of strongly regular modules over a ring which is not necessarily commutative is
introduced. The relation between F-regular, GF-regular and vn-regular modules that are …

Let R be a commutative ring with identity and M a unitary R-module. Some properties of
prime submodules of an R-module M have been discussed. In this paper, we investigate the …

Let R be a commutative ring with non-zero identity and M be a unitary R-module. Let (M) be
the set of all submodules of M, and φ:(M)→(M)∪{∅} be a function. We say that a proper …

Let $ R $ be a commutative ring with identity and let $ M $ be an $ R $-module. A proper
submodule $ P $ of $ M $ is called strongly prime submodule if $(P+ Rx: M) y P $ for $ x, y M …

In this paper, we consider associative rings with unit and unitary modules over these rings.
Let R be a ring and M a right unitary R-module. We denote by J (R) and J (M) the Jacobson …

In this paper, we study modules with the properties (CRE) and (CREE), which are adapted
Zöschinger's modules with the properties. E/and. EE/. It is shown that:(1) a module M has the …