Pseudo Quasi-2-Absorbing Submodules and Some Related Concepts
| Autor: | Haibat K. Mohammad Ali, Omar A. Abdulla |
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| Rok vydání: | 2019 |
| Předmět: | |
| Zdroj: | Ibn AL-Haitham Journal For Pure and Applied Sciences. 32:114-122 |
| ISSN: | 2521-3407 1609-4042 |
| DOI: | 10.30526/32.2.2149 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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