We also obtain numerous classes of monoidsover which indecomposable acts satisfying Condition(P′)are locally cyclic.
📌 3 Key Takeaways
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Objective & Hypothesis:In this paper we consider two different definitions of cover, one of them is Enochs’ notion ofa cover and the other is the one that initiated by Mahmoudi and Renshaw which concernedwith the coessential epimorphisms.
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Key Findings & Data:We show that these definitions are not equivalent inour case and restrict our attention to(P′)-covers (coessential-covers that satisfy Condition(P′)).
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Conclusion & Impact:We also obtain numerous classes of monoidsover which indecomposable acts satisfying Condition(P′)are locally cyclic.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
In this paper we consider two different definitions of cover, one of them is Enochs’ notion ofa cover and the other is the one that initiated by Mahmoudi and Renshaw which concernedwith the coessential epimorphisms. We show that these definitions are not equivalent inour case and restrict our attention to(P′)-covers (coessential-covers that satisfy Condition(P′)). We give a necessary and sufficient condition for a cyclic act to have a(P′)-coverand a sufficient condition for every act to have aP′-cover (Enochs’P′-cover whereP′isthe class ofS-acts satisfying Condition(P′)). We also obtain numerous classes of monoidsover which indecomposable acts satisfying Condition(P′)are locally cyclic.
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Cite This Article
Irannezhad, S., Madanshekaf, A. (2022). On covers of acts over monoidswith Condition(P′). Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 352–361. https://ajindex.com/articles/529618
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