On $GPW$-Flat Acts | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 3، دوره 12، شماره 1، فروردین 2020، صفحه 25-42 اصل مقاله (640.7 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.29252/cgasa.12.1.25 | ||
| نویسندگان | ||
| Hamideh Rashidi1؛ Akbar Golchin2؛ Hossein Mohammadzadeh Saany3 | ||
| 1Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran. | ||
| 2University of Sistan and Baluchestan | ||
| 3Department of Mathematics, University of Sistan and Baluchestan, Zahedan, Iran | ||
| چکیده | ||
| In this article, we present $GPW$-flatness property of acts over monoids, which is a generalization of principal weak flatness. We say that a right $S$-act $A_{S}$ is $GPW$-flat if for every $s \in S$, there exists a natural number $n = n_ {(s, A_{S})} \in \mathbb{N}$ such that the functor $A_{S} \otimes {}_{S}- $ preserves the embedding of the principal left ideal ${}_{S}(Ss^n)$ into ${}_{S}S$. We show that a right $S$-act $A_{S}$ is $GPW$-flat if and only if for every $s \in S$ there exists a natural number $n = n_{(s, A_{S})} \in \mathbb{N}$ such that the corresponding $\varphi$ is surjective for the pullback diagram $P(Ss^n, Ss^n, \iota, \iota, S)$, where $\iota : {}_{S}(Ss^n) \rightarrow {}_{S}S$ is a monomorphism of left $S$-acts. Also we give some general properties and a characterization of monoids for which this condition of their acts implies some other properties and vice versa. | ||
| کلیدواژهها | ||
| $GPW$-flat؛ eventually regular monoid؛ eventually left almost regular monoid | ||
| مراجع | ||
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