Article
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Covers of Finitely Generated Acts over Monoids
Version 1
: Received: 28 March 2024 / Approved: 3 April 2024 / Online: 3 April 2024 (08:28:04 CEST)
How to cite: Zhang, X.; Zhao, T. Covers of Finitely Generated Acts over Monoids. Preprints 2024, 2024040268. https://doi.org/10.20944/preprints202404.0268.v1 Zhang, X.; Zhao, T. Covers of Finitely Generated Acts over Monoids. Preprints 2024, 2024040268. https://doi.org/10.20944/preprints202404.0268.v1
Abstract
In (Semigroup Forum 77: 325-338, 2008) Mahmoudi M. and Renshaw J. solved a study that covers of cyclic $S$-acts over monoids. This article is an attempt to initiate the covers of finitely generated $S$-acts. We give a necessary and sufficient condition for a monoid to have the properties that $n$-generated $S$-acts have strongly flat covers, Condition $(P)$ covers and projective covers. The main conclusions extend some known results. We show also that Condition $(P)$ covers of finitely generated $S$-acts are not unique, unlike the situation for strongly flat covers. Additionally, we demonstrate that the property of Enochs' $\mathcal{X}$-precover of $S$-act $A$, where $\mathcal{X}$ denotes a class of $S$-acts that are closed under isomorphisms.
Keywords
cover; coproduct; finitely generated; $\mathcal{X}$-precover
Subject
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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