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, Omar A.; MOHAMMAD ALI, Haibat K.. Pseudo Quasi-2-Absorbing Submodules and Some Related Concepts. Ibn AL- Haitham Journal For Pure and Applied Science, [S.l.], v. 32, n. 2, p. 114-122, may 2019. ISSN 2521-3407. Available at: <http://jih.uobaghdad.edu.iq/index.php/j/article/view/2149>. Date accessed: 18 june 2019. doi: http://dx.doi.org/10.30526/32.2.2149.
Section
mathematics