Abstract
As a generalization of the maximal sub-module concept, we introduce and investigate the idea of approximately maximal sub-modules in this paper, in which an actual sub-module S of D is named approximately maximal, if whenever a sub-module S ⊆ K ⊆ D implies that K + Soc(D) = D. Numerous features of maximal sub-modules are taken into consideration. Additionally, the term AP-module refers to a module in which each suitable sub-module is roughly maximal. Also, we examine certain characteristics, characterizations, and examples about this class of these modules.
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