Shahid Beheshti University Categories and General Algebraic Structures with Applications 2345-5853 24 1 2026 01 01 Weakly right po-Noetherian ordered semigroups 151 170 105322 10.48308/cgasa.2024.233929.1444 EN Leila Shahbaz Dept. of Mathematics, Faculty of Basic sciences, University of Maragheh, Maragheh, IRAN 0000-0001-6312-6231 Journal Article 2023 11 27 In this paper, we present a new way of defining the property of being WRP-Noetherian by making use of principal right poideals. Additionally, we provide a characterization of WRP-Noetherian ordered semigroups through their $S$-posets. Furthermore, we investigate how the property of being WRP-Noetherian behaves under some semigroup-theoretic constructions, like sub ordered semigroups, and quotients. Specifically, we establish necessary and sufficient conditions for the direct product of two ordered semigroups to be WRP-Noetherian. Ordered semigroup finiteness condition Noetherian ordered semigroup https://cgasa.sbu.ac.ir/article_105322_a53aa0b1bf7c7e2b5e18db176edd6ea3.pdf