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

Authors

XINGLIANG LIANG
YANFENG LUO

DOI

10.3906/mat-1410-26

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

First Page

795

Last Page

809

Recommended Citation

LIANG, XINGLIANG and LUO, YANFENG (2015) "On Condition $(PWP)_{w}$ for $S$-posets," Turkish Journal of Mathematics: Vol. 39: No. 6, Article 1. https://doi.org/10.3906/mat-1410-26
Available at: https://journals.tubitak.gov.tr/math/vol39/iss6/1