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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
De Gruyter
2025-04-01
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| Series: | Open Mathematics |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/math-2025-0136 |
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| Summary: | 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. |
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| ISSN: | 2391-5455 |