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

#### Setareh IRANNEZHAD [1] , Ali MADANSHEKAF [2]

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.
monoids, acts, condition $(P')$, covers
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Primary Language en Mathematics Mathematics Orcid: 0000-0001-7795-2809Author: Setareh IRANNEZHAD Institution: Semnan UniversityCountry: Iran Orcid: 0000-0002-0195-3079Author: Ali MADANSHEKAF Institution: Semnan UniversityCountry: Iran Publication Date : February 6, 2020
 Bibtex @research article { hujms552216, journal = {Hacettepe Journal of Mathematics and Statistics}, issn = {2651-477X}, eissn = {2651-477X}, address = {}, publisher = {Hacettepe University}, year = {2020}, volume = {49}, pages = {352 - 361}, doi = {10.15672/hujms.552216}, title = {On covers of acts over monoids with Condition \$(P')\$}, key = {cite}, author = {IRANNEZHAD, Setareh and MADANSHEKAF, Ali} } APA IRANNEZHAD, S , MADANSHEKAF, A . (2020). On covers of acts over monoids with Condition $(P')$. Hacettepe Journal of Mathematics and Statistics , 49 (1) , 352-361 . DOI: 10.15672/hujms.552216 MLA IRANNEZHAD, S , MADANSHEKAF, A . "On covers of acts over monoids with Condition $(P')$". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 352-361 Chicago IRANNEZHAD, S , MADANSHEKAF, A . "On covers of acts over monoids with Condition $(P')$". Hacettepe Journal of Mathematics and Statistics 49 (2020 ): 352-361 RIS TY - JOUR T1 - On covers of acts over monoids with Condition $(P')$ AU - Setareh IRANNEZHAD , Ali MADANSHEKAF Y1 - 2020 PY - 2020 N1 - doi: 10.15672/hujms.552216 DO - 10.15672/hujms.552216 T2 - Hacettepe Journal of Mathematics and Statistics JF - Journal JO - JOR SP - 352 EP - 361 VL - 49 IS - 1 SN - 2651-477X-2651-477X M3 - doi: 10.15672/hujms.552216 UR - https://doi.org/10.15672/hujms.552216 Y2 - 2018 ER - EndNote %0 Hacettepe Journal of Mathematics and Statistics On covers of acts over monoids with Condition $(P')$ %A Setareh IRANNEZHAD , Ali MADANSHEKAF %T On covers of acts over monoids with Condition $(P')$ %D 2020 %J Hacettepe Journal of Mathematics and Statistics %P 2651-477X-2651-477X %V 49 %N 1 %R doi: 10.15672/hujms.552216 %U 10.15672/hujms.552216 ISNAD IRANNEZHAD, Setareh , MADANSHEKAF, Ali . "On covers of acts over monoids with Condition $(P')$". Hacettepe Journal of Mathematics and Statistics 49 / 1 (February 2020): 352-361 . https://doi.org/10.15672/hujms.552216 AMA IRANNEZHAD S , MADANSHEKAF A . On covers of acts over monoids with Condition $(P')$. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 352-361. Vancouver IRANNEZHAD S , MADANSHEKAF A . On covers of acts over monoids with Condition $(P')$. Hacettepe Journal of Mathematics and Statistics. 2020; 49(1): 361-352.

Authors of the Article
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