On Nearly Prime Submodules of Unitary Modules

Abstract

The aim of this paper is to introduce the notion of nearly prime submodules as a generalization of prime submodules. We investigate some of their basic properties and point out the similarities between these submodules and the prime submodules. We also indicate some applications of nearly prime submodules. These applications show how nearly prime submodules control the structure of modules and they recover earlier relative theorems.

On Radical of Intuitionistic Fuzzy Primary Submodule

“…Also, the spectrum of weakly prime submodule has been investigated in [2]. Following this, the concepts of primal submodules over the noncommutative ring and nearly prime submodules have been presented in [3,4].…”

Uniformly Primal Submodule over Noncommutative Ring

“…e concept of uniformly primal submodules has been introduced and studied by Dauns in [5]. A submodule N of M is called a uniformly primal submodule provided that the set adj(N) � x ∈ R|mRr ⊆ N for some m ∈ M { } is uniformly not prime to N, where the subset B of R is uniformly not right prime to N if there exists an element s ∈ M − N with sRB ⊆ N. In particular, a number of papers concerning primal submodules have been studied by various authors (see, for example, [6][7][8][9][10]). In Section 2, we give some basic results about uniformly primal submodules and show that N 1 , N 2 , .…”