TY - JOUR
AU - Abdulla, Omar A.
AU - Mohammad Ali, Haibat K.
PY - 2019
TI - Pseudo Quasi-2-Absorbing Submodules and Some Related Concepts
JF - Ibn AL- Haitham Journal For Pure and Applied Science; Vol 32 No 2 (2019)
DO - 10.30526/32.2.2149
KW -
N2 - 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.
UR - http://jih.uobaghdad.edu.iq/index.php/j/article/view/2149