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.