SOME REMARKS ON WEAKLY S-LASKERIAN MODULES

The rings considered in this paper are commutative with identity and the modules considered are modules over commutative rings and are unitary. We use R to denote a ring, S to denote a multiplicatively closed subset of R, and M to denote a module over R. We say that M is an S-Laskerian (respectively, a strongly S-Laskerian) R-module if M is an S-finite R-module and for any submodule N of M, either (N: M) meets S or there exist t in S and an S-decomposable (respectively, a strongly S-decomposable) submodule K of M such that tN is a submodule of K and K is contained in N. We say that M is a weakly S-Laskerian (respectively, weakly strongly S-Laskerian) R-module if each S-finite proper submodule of M is an S-Laskerian (respectively, a strongly Laskerian ) R-module. In this paper, we discuss some results on basic properties of weaklly S-Laskerian modules and we extend some of the properties of S-Laskerian modules to weakly S-Laskerian modules.

کلیدواژه ها:

S-Laskerian module ، strongly S-Laskerian module ، weakly S-Laskerian module ، weakly strongly S-Laskerian module