Covers of Finitely Generated Acts over Monoids

Xiaoqin Zhang () and Tingting Zhao
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Xiaoqin Zhang: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
Tingting Zhao: College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China

Mathematics, 2024, vol. 12, issue 12, 1-12

Abstract: This paper attempts to initiate the study of covers of finitely generated S -acts over monoids. We provide necessary and sufficient conditions for a monoid to ensure that n -generated S -acts have strongly flat covers, Condition ( P ) covers, and projective covers. The main conclusions extend some known results. We also show that Condition ( P ) covers of finitely generated S -acts are not unique, unlike strongly flat covers. Additionally, we demonstrate the property of Enochs’ X -precover of S -act A , where X denotes a class of S -acts that are closed under isomorphisms.

Keywords: cover; coproduct; finitely generated; X -precover (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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