Eventually semi strongly torsion free acts over monoids [Articol]

Abstract

We present eventually semi strongly torsion freeness of acts over monoids, which is a generalization of strongly torsion freeness. We say that a right S-act AS is eventually semi strongly torsion free if for every s 2 S, there exists a natural number n = n(s;AS) 2 N such that asn = a0sn for any a; a0 2 AS, implies ar = a0r and rsn = sn, for some r 2 S. We show that eventually semi strongly torsion freeness implies GPWflatness. Also we give some general properties of eventually semi strongly torsion freeness and characterizations of monoids for which this property of their acts implies some other properties and vice versa.