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PURE – SUPPLEMENTED MODULES | ||
| Iraqi Journal of Science | ||
| Article 1, Volume 53, Issue 4, 2012, Pages 882-886 | ||
| Authors | ||
| Yasen Sahira Mahmood; Wasan Khalid Hasan | ||
| Abstract | ||
| Let R be an associative ring with identity and M be unital non zero right R- module . M is called H– supplemented module if given any submodule A of M 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 for H– supplemented which is called pure– supplemented module. An R- module M is called pure– supplemented module if given any submodule A of M there 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 of M such that << and << . | ||
| Keywords | ||
| Small submodule; Supplementod module; Pure module; lifting module | ||
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