Quasi-projective covers of right $S$-acts
In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a uni...
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Shahid Beheshti University
2014-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
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| Online Access: | http://www.cgasa.ir/article_6482_f25fef016a297f3166ecafec83d649d8.pdf |
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doaj-276965e5de144a699454aba2ebfac0bd2020-11-24T22:21:02ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612014-07-012137456482Quasi-projective covers of right $S$-actsMohammad Roueentan0Majid Ershad1Department of Mathematics, College of Science, Shiraz University, Shiraz 71454, Iran.Department of Mathematics, College of Science, Shiraz University, Shiraz 71454, Iran.In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that every right act has a projective cover. http://www.cgasa.ir/article_6482_f25fef016a297f3166ecafec83d649d8.pdfProjectivequasi-projectiveperfectsemiperfectcover |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Mohammad Roueentan Majid Ershad |
| spellingShingle |
Mohammad Roueentan Majid Ershad Quasi-projective covers of right $S$-acts Categories and General Algebraic Structures with Applications Projective quasi-projective perfect semiperfect cover |
| author_facet |
Mohammad Roueentan Majid Ershad |
| author_sort |
Mohammad Roueentan |
| title |
Quasi-projective covers of right $S$-acts |
| title_short |
Quasi-projective covers of right $S$-acts |
| title_full |
Quasi-projective covers of right $S$-acts |
| title_fullStr |
Quasi-projective covers of right $S$-acts |
| title_full_unstemmed |
Quasi-projective covers of right $S$-acts |
| title_sort |
quasi-projective covers of right $s$-acts |
| publisher |
Shahid Beheshti University |
| series |
Categories and General Algebraic Structures with Applications |
| issn |
2345-5853 2345-5861 |
| publishDate |
2014-07-01 |
| description |
In this paper $S$ is a monoid with a left zero and $A_S$ (or $A$) is a unitary right $S$-act. It is shown that a monoid $S$ is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right $S$-act is quasi-projective. Also it is shown that if every right $S$-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that every right act has a projective cover. |
| topic |
Projective quasi-projective perfect semiperfect cover |
| url |
http://www.cgasa.ir/article_6482_f25fef016a297f3166ecafec83d649d8.pdf |
| work_keys_str_mv |
AT mohammadroueentan quasiprojectivecoversofrightsacts AT majidershad quasiprojectivecoversofrightsacts |
| _version_ |
1725772611849289728 |