Classes of modules closed under projective covers
In this work, we study some classes of modules closed under submodules, quotients, and projective covers, even if the left projective cover of an arbitrary left module not always exists. We obtain a characterization of artinian principal ideal rings when the class of left RR-modules closed under sub...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-04-01
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| Series: | Open Mathematics |
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| Online Access: | https://doi.org/10.1515/math-2025-0136 |
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| author | Cejudo-Castilla César García-Ramírez Ángel Raúl Montalvo Ivan Fernando Vilchis |
| author_facet | Cejudo-Castilla César García-Ramírez Ángel Raúl Montalvo Ivan Fernando Vilchis |
| author_sort | Cejudo-Castilla César |
| collection | DOAJ |
| description | In this work, we study some classes of modules closed under submodules, quotients, and projective covers, even if the left projective cover of an arbitrary left module not always exists. We obtain a characterization of artinian principal ideal rings when the class of left RR-modules closed under submodules and projective covers and the class of left RR-modules closed under quotients and projective covers coincide. Also, for commutative rings, we characterize noetherian rings in which every cyclic module is quasi-injective. |
| format | Article |
| id | doaj-art-2d3bc1683778475f9998497a3103f2b7 |
| institution | OA Journals |
| issn | 2391-5455 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Open Mathematics |
| spelling | doaj-art-2d3bc1683778475f9998497a3103f2b72025-08-20T02:11:55ZengDe GruyterOpen Mathematics2391-54552025-04-012311637164810.1515/math-2025-0136Classes of modules closed under projective coversCejudo-Castilla César0García-Ramírez Ángel Raúl1Montalvo Ivan Fernando Vilchis2Department of Mathematics, Av. San Claudio y 18 Sur S/N, Benemérita Universidad Autónoma de Puebla, Puebla, MexicoDepartment of Mathematics, Av. San Claudio y 18 Sur S/N, Benemérita Universidad Autónoma de Puebla, Puebla, MexicoDepartment of Mathematics, Av. San Claudio y 18 Sur S/N, Benemérita Universidad Autónoma de Puebla, Puebla, MexicoIn this work, we study some classes of modules closed under submodules, quotients, and projective covers, even if the left projective cover of an arbitrary left module not always exists. We obtain a characterization of artinian principal ideal rings when the class of left RR-modules closed under submodules and projective covers and the class of left RR-modules closed under quotients and projective covers coincide. Also, for commutative rings, we characterize noetherian rings in which every cyclic module is quasi-injective.https://doi.org/10.1515/math-2025-0136projective coversartinian principal ideal ringsclasses of modulesqf-rings16d4016d8016l60 |
| spellingShingle | Cejudo-Castilla César García-Ramírez Ángel Raúl Montalvo Ivan Fernando Vilchis Classes of modules closed under projective covers Open Mathematics projective covers artinian principal ideal rings classes of modules qf-rings 16d40 16d80 16l60 |
| title | Classes of modules closed under projective covers |
| title_full | Classes of modules closed under projective covers |
| title_fullStr | Classes of modules closed under projective covers |
| title_full_unstemmed | Classes of modules closed under projective covers |
| title_short | Classes of modules closed under projective covers |
| title_sort | classes of modules closed under projective covers |
| topic | projective covers artinian principal ideal rings classes of modules qf-rings 16d40 16d80 16l60 |
| url | https://doi.org/10.1515/math-2025-0136 |
| work_keys_str_mv | AT cejudocastillacesar classesofmodulesclosedunderprojectivecovers AT garciaramirezangelraul classesofmodulesclosedunderprojectivecovers AT montalvoivanfernandovilchis classesofmodulesclosedunderprojectivecovers |