On subprojectivity domains of g-semiartinian modules

The aim of this paper is to reveal the relationship between the proper class generated projectively by g-semiartinian modules and the subprojectivity domains of g-semiartinian modules. A module M is called g-semiartinian if every nonzero homomorphic image of M has a singular simple submodule. It is proven that every g-semiartinian right R-module has an epic projective envelope if and only if R is a right PS ring if and only if every subprojectivity domain of any g-semiartinian right R-module is closed under submodules. A g-semiartinian module whose domain of subprojectivity as small as possible is called gsap-indigent. We investigated the structure of rings whose (simple, coatomic) g-semiartinian right modules are gsap-indigent or projective. Furthermore, over right PS rings, necessary and sufficient condition to be gsap-indigent module was determined.