S-Noetherian rings, modules and their generalizations
Let R be a commutative ring with identity, M an R-module and S ⊆ R a multiplicative set. Then M is called S-finite if there exist an s ∈ S and a finitely generated submodule N of M such that sM ⊆ N. Also, M is called S-Noetherian if each submodule of M is S-finite. A ring R is called S-Noetherian if...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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University Constantin Brancusi of Targu-Jiu
2023-09-01
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| Series: | Surveys in Mathematics and its Applications |
| Subjects: | |
| Online Access: | https://www.utgjiu.ro/math/sma/v18/p18_13.pdf |
| Summary: | Let R be a commutative ring with identity, M an R-module and S ⊆ R a multiplicative set. Then M is called S-finite if there exist an s ∈ S and a finitely generated submodule N of M such that sM ⊆ N. Also, M is called S-Noetherian if each submodule of M is S-finite. A ring R is called S-Noetherian if it is S-Noetherian as an R-module. This paper surveys the most recent developments in describing the structural properties of S-Noetherian rings, S-Noetherian modules and their generalizations. Some interesting constructed examples of S-Noetherian rings and modules are also presented. |
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| ISSN: | 1843-7265 1842-6298 |