On subprojectivity domains of g-semiartinian modules

Abstract

<jats:p> 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 [Formula: see text] is called g-semiartinian if every nonzero homomorphic image of [Formula: see text] has a singular simple submodule. It is proven that every g-semiartinian right [Formula: see text]-module has an epic projective envelope if and only if [Formula: see text] is a right PS ring if and only if every subprojectivity domain of any g-semiartinian right [Formula: see text]-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. </jats:p>

Rings Whose Pure-Projective Modules Have Maximal or Minimal Projectivity Domain

“…Let R be an associative ring with identity throughout the article, and unless otherwise indicated, any module be a right R-module. Projectivity has been investigated from various angles in the recent studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15]. The class {Y ∈ Mod-R : X is Y -projective} for a module X is referred to as the projectivity domain of X and is represented by Pr −1 (X) [16].…”