Relatively divisible and relatively flat objects in exact categories

Abstract

We continue our study of relatively divisible and relatively flat objects in exact categories in the sense of Quillen with several applications to exact structures on finitely accessible additive categories and module categories. We derive consequences for exact structures generated by the simple modules and the modules with zero Jacobson radical.

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].…”