Pseudo Quasi-2-Absorbing Submodules and Some Related Concepts

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Omar A. Abdulla
Haibat K. Mohammad Ali

Abstract

Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H or rs∈[H:A], and a proper submodule H of an R-module A is called quasi-prime , if rsa∈H, where r,s∈R,a∈A, implies that either ra∈H or sa∈H. This led us to introduce the concept pseudo quasi-2-absorbing submodule, as a generalization of both concepts above, where a proper submodule H of an R-module A is called a pseudo quasi-2-absorbing submodule of A, if whenever rsta∈H,where r,s,t∈R,a∈A, implies that either rsa∈H+soc(A) or sta∈H+soc(A) or rta∈H+soc(A), where soc(A) is socal of an R-module A. Several basic properties, examples and characterizations of this concept are given. Moreover, we investigate relationships between pseudo quasi-2-absorbing submodule and other classes of submodules.

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How to Cite
Abdulla, O. A., & Mohammad Ali, H. K. (2019). Pseudo Quasi-2-Absorbing Submodules and Some Related Concepts. Ibn AL-Haitham Journal For Pure and Applied Sciences, 32(2), 114–122. https://doi.org/10.30526/32.2.2149
Section
mathematics