On regular torsionless S-posets

Abstract

This paper shall be concerned with the notion of regular torsionless in the category of S-posets. Besides elementary basic properties of regular torsionless S-posets, we consider cyclic regular torsionless S-posets and also study when regular torsionless property is preserved under coproducts. Then we characterize pomonoids over which all free or projective S-posets are regular torsionless. Finally, we present conditions on S which follow if all regular torsionless S-posets are principally weakly po-flat, weakly po-flat, strongly flat, or projective.