PURE – SUPPLEMENTED MODULES - Yasen, Sahira (Iraqi Journal of Science, 2024)
Let R be an associative ring with identity and M be unital non zero right Rmodule. M is called H– supplemented module if given any submodule A ofM there exist a direct summend submodule D of M such that M = A+X iff M=D+X where X is a submodule of M. In this paper we will give a generalization forH– supplemented which is called pure– supplemented module. An R- moduleM is called pure– supplemented module if given any submodule A of Mthere exists a pure submodule P of M such that M = A+X iff M= P+X.Equivalently , for every submodule A of M there exist a pure submodule P ofM such thatPA + P<<PMandAA + P<<