Covers of Finitely Generated Acts over Monoids

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%22%2C%22default_operator%22%3A%22AND%22%7D%7D%7D"> <named-content content-type="equation"> <mml:math id="mm9999"> <mml:semantics> <mml:mi mathvariant="script">X</mml:mi> </mml:semantics> </mml:math> </named-content>-precover