Categories and General Algebraic Structures with Applications

Categories and General Algebraic Structures with Applications

On a generalization of Conditions $(PWP)$ and $(PWP)_w$

Articles in Press

Document Type : Research Paper

Authors
Hamideh Rashidi 1
Roghaieh Khosravi 2
1 Department of Mathematics, Faculty of Science, University of Jiroft, Jiroft, Iran
2 Department of Mathematics, Fasa University, Fasa, Fars, Iran
10.48308/cgasa.2025.241191.1566
Abstract
In their foundational work (Commun. Algebra, Vol. 37, No. 6, pp. 1995–2007), Golchin and Rezaei formulated the Conditions $(PWP)$ and $(PWP)_w$. Building on their framework, we present the generalized versions denoted $(GPWP)$ and $(G-(PWP)_w)$. We prove that the former condition entails the latter, although the converse does not necessarily hold. We explore several fundamental properties of these generalized conditions and establish necessary and sufficient criteria under which an amalgamated coproduct satisfies these conditions. Additionally, we examine pomonoids $S$ for which all cyclic or Rees factor $S$-posets fulfill Condition $(G-(PWP)_w)$ or $(GPWP)$, respectively. We further analyze pomonoids where every Rees factor $S$-poset satisfying one of the proposed conditions exhibits a particular structural property. Finally, we study the behavior of direct products of $S$-posets that satisfy these Conditions.
Keywords
Condition $(G-(PWP)_w)$
Condition $(PWP)$
eventually strongly left annihilating
eventually strongly left stabilizing
Subjects
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Categories and General Algebraic Structures with Applications

Articles in Press, Accepted Manuscript
Available Online from 11 October 2026