Submodules Satisfying the Uniformly Classical S-Primary Property

Abstract

We define uniformly classical S-primary submodules, where S is a multiplicatively closed subset. A submodule W of an H-module E with (W:HE)boolean AND S = & empty; is said to be a uniformly classical S-primary submodule if there exists s is an element of S and k is an element of Z+ such that whenever eta gamma nu is an element of W for eta, gamma is an element of H, nu is an element of E, then s eta nu is an element of W or (s gamma)k nu is an element of W. We investigate many properties of this new type of submodules and give relations with the other submodules. We provide various characterizations of this class of submodules in terms of other submodules and ideals. Moreover, we study the notion under homomorphisms, in factor modules, Cartesian product, localization, idealization, and amalgamation modules along an ideal with respect to a homomorphism.