Soc-QP2- Absorbing Submodules

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  for , , implies one of two possibilities  or   or . The qualities, characterizations, and examples of this innovative notion are described.