On Condition (PW P)w for S-posets

Abstract

Golchin and Rezaei (Commun Algebra 2009; 37: 1995 2007) introduced the weak version of Condition (PW P) for S -posets, called Condition (PW P)w . In this paper, we continue to study this condition. We first present a necessary and sufficient condition under which the S -poset A(I) satisfies Condition (PW P)w . Furthermore, we characterize pomonoids S over which all cyclic (Rees factor) S -posets satisfy Condition (PW P)w , and pomonoids S over which all Rees factor S -posets satisfying Condition (PW P)w have a certain property. Finally, we consider direct products of S -posets satisfying Condition (PW P)w .