RD-projective module whose subprojectivity domain is minimal

Abstract

A p-indigent module is one that is subprojective only to projective modules. An RDprojective module is subprojective to any torsionfree (and flat) module. An RD-projective module T is called rdp-indigent if it is subprojective only to torsionfree modules. In this work, we consider the structure of SRDP rings whose (simple) RD-projective right Rmodules are rdp-indigent or torsionfree. Moreover, new characterizations of P-coherent rings and torsionfree rings are presented by subprojectivity domains.

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].…”