Significance of Modules with Ascending Chain Condition Which Corresponds of Definite Sorts of Annihilator

A left or right module M over a ring with identity e such that multiplication by e is the transformation m ?em(respectively m ?me for right modules ), m?M is the identity automorphism of the group M over a commutative ring R with unit represents "n ? acc of d ? colons" where unitary module?s sub module P and the ascending chain R whose elements that hold distinct sequence (an ) n such that P : a1 ? a1a2 ?........ stabilizes . Specially , in this paper we have tried to focus the acc on d ? colons and establish that d ? colons represents the acc on n ? generated submodules for every n , simplifying "Commutative Rings with ACC on n ?Generated Ideals by W. Heinzer and David Lantz? a ? generalized Nakayma?s Lemma for these modules. Moreover it has showed that every R ? module R I for a Noetherian ring R involves n ? acc and a sufficient condition for the acc on ideals to the polynomial ring. The goal of this paper is to locate on modules with acc which represents of certain sorts of annihilators and n ? acc on d ? colons.