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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2020 / Cilt: 49 - Sayı: 1

On covers of acts over monoids with Condition $(P')$

Setareh IRANNEZHAD
Ali MADANSHEKAF
Sayfa
352–361
Yayın Tarihi
2020-02-06
DOI
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We also obtain numerous classes of monoids over which indecomposable acts satisfying Condition $(P')$ are locally cyclic.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper we consider two different definitions of cover, one of them is Enochs' notion of a cover and the other is the one that initiated by Mahmoudi and Renshaw which concerned with the coessential epimorphisms.
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Temel Bulgular & Veri:We show that these definitions are not equivalent in our case and restrict our attention to $(P')$-covers (coessential-covers that satisfy Condition $(P')$).
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Sonuç & Katkı:We also obtain numerous classes of monoids over which indecomposable acts satisfying Condition $(P')$ are locally cyclic.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:monoids · acts · condition $(P')$

Abstract

In this paper we consider two different definitions of cover, one of them is Enochs' notion of a cover and the other is the one that initiated by Mahmoudi and Renshaw which concerned with the coessential epimorphisms. We show that these definitions are not equivalent in our 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 $(P')$-cover and a sufficient condition for every act to have a $\mathcal{P'}$-cover (Enochs' $\mathcal{P'}$-cover where $\mathcal{P'}$ is the class of $S$-acts satisfying Condition $(P')$). We also obtain numerous classes of monoids over which indecomposable acts satisfying Condition $(P')$ are locally cyclic.

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Bu Makaleye Atıf Yap

IRANNEZHAD, S., MADANSHEKAF, A. (2020). On covers of acts over monoids with Condition $(P')$. Hacettepe Journal of Mathematics and Statistics, Cilt: 49 - Sayı: 1, 352–361. https://ajindex.com/articles/669316

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Kaynakça (13)

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