Turkish Journal of Computer and Mathematics Education
Journal license

Journal

Turkish Journal of Computer and Mathematics Education


Volume
& Issue

Volume 13, Issue 3


Published
on


Pages

761-770


DOI

Article

Soc-QP2- Absorbing Submodules


Authors

Reem Taha Abdulqader Affiliation:
Dept. of Mathematics, College of Computer Science and Mathematics, University of Tikrit, Tikrit, Iraq
, Zinah Taha Abdulqader Affiliation:
Dept. of Mathematics, College of Education for women, University of Tikrit, Tikrit, Iraq
, Haibat K. Mohammadali Affiliation:
Dept. of Mathematics, College of Computer Science and Mathematics, University of Tikrit, Tikrit, Iraq
and Akram S. Mohammed Affiliation:
Dept. of Mathematics, College of Computer Science and Mathematics, University of Tikrit, Tikrit, Iraq


Abstract

Let R be a unitary left R-module and T be a self-identifiable commutative ring. We introduce and analyze the idea of socle-quasi-primary-2-absorbing submodules, which is a combination of primary and 2-absorbing submodules that considers a proper submodule L of an R-module. Socle-quasi-primary is abbreviated as T. T is made up of two absorbing submodules (Soc-QP2-absorbing), if whenever $rst \in L$ for $r, s \in R$, $t \in T$, implies one of two possibilities: $rt \in T - \operatorname{rad}(L) + \operatorname{soc}(T)$ or $st \in T - \operatorname{rad}(L) + \operatorname{soc}(T)$ or $rs \in \sqrt{[L + \operatorname{soc}(T):_R T]}$. The qualities, characterizations, and examples of this innovative notion are described.


Keywords

Prime submodules, Primary submodules, 2-absorbing submodules, Socle of modules, Radical of submodules, Multiplication modules, Non-singular modules


Citation

Abdulqader, R. T., Abdulqader, Z. T., Mohammadali, H. K., & Mohammed, A. S. (2022). Soc-QP2- absorbing submodules. Turkish Journal of Computer and Mathematics Education, 13(3), 761–770.

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