A study on sdfa -prime submodules

This paper introduces square-difference factor absorbing prime submodules, abbreviated as sdfa-prime submodules, as a new class of submodules over commutative rings. The ideal-theoretic properties of sdfa-prime structures are established, followed by an extension to general modules, comparing sdfa-prime and strong sdfa-prime submodules with several established submodule classes. Furthermore, we analyze their behavior under standard algebraic constructions, including localization, homomorphic images, quotient structures, direct sums, and Nagata's idealization. As an application, characterizations of von Neumann regular modules are established through localization.