The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies this it is relationship to previous generalizationsm especially 2-Absorbing submodule submodule, addition studying most important Propositions, charactarizations Examples. Now research, which considered a continuation definition tha...

‎Let $R$ be commutative ring with identity and $M$ be an $R$-module‎. ‎The zero divisor graph of $M$ is denoted $Gamma{(M)}$‎. ‎In this study‎, ‎we are going to generalize the zero divisor graph $Gamma(M)$ to submodule-based zero divisor graph $Gamma(M‎, ‎N)$ by replacing elements whose product is zero with elements whose product is in some submodules $N$ of $M$‎. ‎The main objective of this pa...

Our dual notions “locally injective” and “locally projective” modules in Mod-R are good tools to study the relations between the singular, respectively cosingular, submodule of Hom R(M, W ) and the total Tot (M, W ). These notions have further interesting properties.

The target of this study is to observe some of the algebraic structures of a single valued neutrosophic set. So, we introduce the concept of a neutrosophic submodule of a given classical module and investigate some of the crucial properties and characterizations of the proposed concept.

Let φ be a Drinfeld module of generic characteristic, and let X be a sufficiently generic affine subvariety of Ga. We show that the intersection of X with a finite rank φ-submodule of Ga is finite. Mathematics Subject Classification Number: Primary 11G09; Secondary 11G10.

A new kind of fuzzy module over a fuzzy ring is introduced by generalizing Yuan and Lee's definition of the fuzzy group and Aktaş and Çağman's definition of fuzzy ring. The concepts of fuzzy submodule, and fuzzy module homomorphism are studied and some of their basic properties are presented analogous of ordinary module theory.

The object of this paper is to study the relationship between certain projective modules and their endomorphism rings. Specifically, the basic problem is to describe the projective modules whose endomorphism rings are (von Neumann) regular, local semiperfect, or left perfect. Call a projective module regular if every cyclic submodule is a direct summand. Thus a ring is a regular module if it is...