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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.01646 |
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| _version_ | 1866915782966902784 |
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| author | Adarbeh, Mohammad Saleh, Mohammad |
| author_facet | Adarbeh, Mohammad Saleh, Mohammad |
| contents | In this article, we introduce the notion of uniformly S-projective (u-S-projective) relative to a module. Let S be a multiplicative subset of a ring R and M an R-module. An R-module P is said to be u-S-projective relative to M if for any u-S-epimorphism f : M \to N, the induced map HomR(P, f ): HomR(P, M ) \to HomR(P, N ) is a u-S-epimorphism. Dually, we also introduce u-S-injective relative to a module. Some properties of these notions are discussed. Several characterizations of u-S-semisimple modules are given in terms of these notions. The notions of u-S-quasi-projective and u-S-quasi-injective modules are also introduced, and some of their properties are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01646 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniformly S-projective relative to a module and its dual Adarbeh, Mohammad Saleh, Mohammad Commutative Algebra In this article, we introduce the notion of uniformly S-projective (u-S-projective) relative to a module. Let S be a multiplicative subset of a ring R and M an R-module. An R-module P is said to be u-S-projective relative to M if for any u-S-epimorphism f : M \to N, the induced map HomR(P, f ): HomR(P, M ) \to HomR(P, N ) is a u-S-epimorphism. Dually, we also introduce u-S-injective relative to a module. Some properties of these notions are discussed. Several characterizations of u-S-semisimple modules are given in terms of these notions. The notions of u-S-quasi-projective and u-S-quasi-injective modules are also introduced, and some of their properties are discussed. |
| title | Uniformly S-projective relative to a module and its dual |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2509.01646 |