Article
Soc-QP2- Absorbing Submodules
Authors
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
Citation
Published by: Engineering Journals


