Dr. Rehana Parvin, Momotaz Katun, Dr. Mst. Rashida Pervin
Abstract: 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 ), mM is the identity automorphism of the group M over a commutative ring R with unit represents n acc of d colons where unitary modules 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 Nakaymas 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.
Keywords: n-acc, annihilator, d-colons