A submodule Ϝ of an R-module Ε is called small in Ε if whenever, for some submodule W of
Ε, implies. In this paper, we introduce the notion of Ζ-small submodule, where a proper …

The main goal of this paper is to give a new generalizations for two important classes in the
category of modules, namely the class of small submodules and the class of hollow …

We introduce and study the concept of D-essential submodules and its dual concept, F-small
submodules, where D and F are arbitrary submodules of a module M. These two notions are …

The purpose of this paper is to introduce new concepts in a module over a ring, the first one
is called e*-small essential submodule, which is a generalization of the small submodule …

In this work, we introduce and study the concept of small-singular submodules as a
generalization of the singular submodules. A number of properties and characterization of …

The present study introduces the concept of J-pure submodules as a generalization of pure
submodules. We study some of its basic properties and by using this concept we define the …

In this work, we give generalizations for the concepts essential submodule and uniform
module. We call an R-submodule N of M semi-essential if N∩ P≠ 0 for each nonzero prime …

In this paper we introduce a new generalization of small submodules, namely γ-small
submodules. We call a submodule K of a module M, γ-small provided M= K+ L with M/L …

Let be a ring with identity and be a submodule of a left-module. A submodule of is called-
small in denoted by, in case for any submodule of, implies. Submodule of is called semi-T …

T المقاسات الرفع المجوفة من النمط Page 1 Yaseen and Elewi Iraqi Journal of Science, 2019, Vol.60,
No.11, pp: 2486-2489 DOI: 10.24996/ijs.2019.60.11.20 …