In this paper, we study the primal submodules of a module over a commutative ring with non-
zero identity. We generalize the primal decomposition of ideals (see [2]) to that of …

We investigate preenvelopes and precovers in the category _ RE RE of short exact
sequences of left R-modules. Let CC be a class of left R-modules. We prove that:(1) A_ 1 …

Let 𝑅 be a ring with identity. Recall that a submodule 𝑁 of a left 𝑅-module 𝑀 is called
strongly essential if for any nonzero subset 𝑋 of 𝑀, there is 𝑟∈ 𝑅 such that (0≠) 𝑟𝑋⊆ 𝑁 …

Let ℒ be a class of right modules, whenever covers and envelopes exist, we show that if ℒ is
closed under extensions and direct summands, then P (ℒ), the class of all ℒ-projective right …

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 …

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 …

It is known that rings and modules over rings are related algebraic structures. Moreover,
near rings and modules over near rings are generalized algebraic structures of rings and …

In this work we introduce the concept of rationally injective module, which is a proper
generalization of (essentially)-injective modules. Several properties and characterizations …

Throughout this paper R represents an associative ring with identity and M is unitary right R-
module, the purpose of this paper is to study a new concept, named s-closed submodules. It …