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| Format: | Preprint |
| Veröffentlicht: |
2025
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| Online-Zugang: | https://arxiv.org/abs/2510.10170 |
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| _version_ | 1866910080657522688 |
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| author | adarbeh, Mohammad Saleh, Mohammad |
| author_facet | adarbeh, Mohammad Saleh, Mohammad |
| contents | In this paper, we introduce the notion of uniformly S-pseudo-projective (u-S-pseudo-projective) modules as a generalization of u-S-projective modules. Let R be a ring and S a multiplicative subset of R. An R-module P is said to be u-S-pseudo-projective if for any submodule K of P, there is s\in S such that for any u-S-epimorphism f:P\to \frac{P}{K}, sf can be lifted to an endomorphism g:P\to P. We prove that an R-module M is u-S-quasi-projective if and only if M\oplus M is u-S-pseudo-projective. Also, we prove that if A\oplus B is u-S-pseudo-projective, then any u-S-epimorphism f:A\to B u-S-splits. We give characterizations of certain classes of rings, such as u-S-semisimple and strongly S-perfect rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_10170 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniformly S-pseudo-projective modules adarbeh, Mohammad Saleh, Mohammad Commutative Algebra In this paper, we introduce the notion of uniformly S-pseudo-projective (u-S-pseudo-projective) modules as a generalization of u-S-projective modules. Let R be a ring and S a multiplicative subset of R. An R-module P is said to be u-S-pseudo-projective if for any submodule K of P, there is s\in S such that for any u-S-epimorphism f:P\to \frac{P}{K}, sf can be lifted to an endomorphism g:P\to P. We prove that an R-module M is u-S-quasi-projective if and only if M\oplus M is u-S-pseudo-projective. Also, we prove that if A\oplus B is u-S-pseudo-projective, then any u-S-epimorphism f:A\to B u-S-splits. We give characterizations of certain classes of rings, such as u-S-semisimple and strongly S-perfect rings. |
| title | Uniformly S-pseudo-projective modules |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2510.10170 |