On Condition $(PWP)_{w}$ for $S$-posets

Authors : Xingliang Liang, Yanfeng Luo

Pages : 795-809

View : 11 | Download : 10

Publication Date : 9999-12-31

Article Type : Makaleler

Abstract :Golchin and Rezaei (Commun Algebra 2009; 37: 1995--2007) introduced the weak version of Condition $(PWP)$ for $S$-posets, called Condition $(PWP)_{w}$. 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 $(PWP)_{w}$. Furthermore, we characterize pomonoids $S$ over which all cyclic (Rees factor) $S$-posets satisfy Condition $(PWP)_{w}$, and pomonoids $S$ over which all Rees factor $S$-posets satisfying Condition $(PWP)_{w}$ have a certain property. Finally, we consider direct products of $S$-posets satisfying Condition $(PWP)_{w}$.
Keywords : Condition $(PWP)_{w}$, $S$-poset, Rees factor $S$-poset, direct product