Classification of monoids by Condition $(PWP_{ssc})$ | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 9، دوره 12، شماره 1، فروردین 2020، صفحه 175-197 اصل مقاله (652.34 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.12.1.175 | ||
| نویسندگان | ||
| Pouyan Khamechi؛ Hossein Mohammadzadeh Saany؛ Leila Nouri | ||
| Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran | ||
| چکیده | ||
| Condition $(PWP)$ which was introduced in (Laan, V., {\it Pullbacks and flatness properties of acts I}, Commun. Algebra, 29(2) (2001), 829-850), is related to flatness concept of acts over monoids. Golchin and Mohammadzadeh in ({\it On Condition $(PWP_E)$}, Southeast Asian Bull. Math., 33 (2009), 245-256) introduced Condition $(PWP_E)$, such that Condition $(PWP)$ implies it, that is, Condition $(PWP_E)$ is a generalization of Condition $(PWP)$. In this paper we introduce Condition $(PWP_{ssc})$, which is much easier to check than Conditions $(PWP)$ and $(PWP_E)$ and does not imply them. Also principally weakly flat is a generalization of this condition. At first, general properties of Condition $(PWP_{ssc})$ will be given. Finally a classification of monoids will be given for which all (cyclic, monocyclic) acts satisfy Condition $(PWP_{ssc})$ and also a classification of monoids $S$ will be given for which all right $S$-acts satisfying some other flatness properties have Condition $(PWP_{ssc})$. | ||
| کلیدواژهها | ||
| $S$-act؛ Flatness properties؛ Condition $(PWP_{ssc})$؛ semi-cancellative؛ $e$-cancellative | ||
| مراجع | ||
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