Uniformly S-essential submodules and uniformly S-injective uniformly S-envelopes
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912830926618624 |
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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-essential (u-S-essential) submodules. Let R be a commutative ring and S a multiplicative subset of R. A submodule K of an R-module M is said to be u-S-essential in M if for any submodule L of M, s1(K \cap L) = 0 for some s1 \in S implies s2L = 0 for some s2 \in S. Several properties of this notion are studied. The notions of a u-S-uniform module and a u-S-injective u-S-envelope are also introduced, and we show that these notions are characterized by u-S-essential submodules. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_01638 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniformly S-essential submodules and uniformly S-injective uniformly S-envelopes Adarbeh, Mohammad Saleh, Mohammad Commutative Algebra In this paper, we introduce the notion of uniformly S-essential (u-S-essential) submodules. Let R be a commutative ring and S a multiplicative subset of R. A submodule K of an R-module M is said to be u-S-essential in M if for any submodule L of M, s1(K \cap L) = 0 for some s1 \in S implies s2L = 0 for some s2 \in S. Several properties of this notion are studied. The notions of a u-S-uniform module and a u-S-injective u-S-envelope are also introduced, and we show that these notions are characterized by u-S-essential submodules. |
| title | Uniformly S-essential submodules and uniformly S-injective uniformly S-envelopes |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2509.01638 |