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On Rees Factor $\mathbf{S}$-Posets Satisfying Conditions $\mathbf{(PWP_{E})}$ or $\mathbf{(PWP_E)_{w}}$ | ||
| Journal of Mahani Mathematical Research | ||
| دوره 12، شماره 2 - شماره پیاپی 25، مرداد 2023، صفحه 529-546 اصل مقاله (533.3 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22103/jmmr.2023.19514.1267 | ||
| نویسندگان | ||
| Zohre Khaki؛ Hossein Mohammadzadeh Saany* ؛ Leila Nouri | ||
| Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran | ||
| چکیده | ||
| Golchin and Rezaei introduced conditions $(PWP)$ and\linebreak $(PWP)_{w}$ in (Subpullbacks and flatness properties of $S$-posets). In this paper, we introduce conditions $(PWP_{E})$ and $(PWP_{E})_{w}$ as generalizations of these conditions, respectively, and show that the relevant implications are strict. In general, we observe that condition $(PWP_{E})_{w}$ follows from condition $(PWP_{E})$, but not conversely. Also, we prove that principal weak po-flatness follows from condition $(PWP_{E})_{w}$, but not conversely. Then, we obtain some general properties of conditions $(PWP_{E})$ and $(PWP_{E})_{w}$, and find sufficient and necessary conditions for the $S$-poset $A(I)$ to satisfy these conditions. Finally, we find conditions on a pomonoid $S$ under which a cyclic or Rees factor $S$-poset satisfies condition $(PWP_{E})$ or condition $(PWP_{E})_{w}$. Thereby, we present some homological classifications of pomonoids over which each of the conditions $(PWP_{E})$ and $(PWP_{E})_{w}$ implies a specific property, and vice versa, for Rees factor $S$-posets. | ||
| کلیدواژه‌ها | ||
| pomonoid؛ $S$-posets؛ Conditions $(PWP_{E})$ and $(PWP_{E})_{w}$؛ Rees factor $S$-posets | ||
| مراجع | ||
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