Some remarks on $S$-Noetherian modules
UDC 512.5 We study several properties and applications of the $S$-Noetherian rings and modules. It is proved that an $S$-Artinian ring is $S$-Noetherian provided that $S$ contains no zero divisors of the module. Furthermore, it is shown that associated primes exist in modul...
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| Date: | 2025 |
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| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Institute of Mathematics, NAS of Ukraine
2025
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| Online Access: | https://umj.imath.kiev.ua/index.php/umj/article/view/7907 |
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| Journal Title: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Summary: | UDC 512.5
We study several properties and applications of the $S$-Noetherian rings and modules. It is proved that an $S$-Artinian ring is $S$-Noetherian provided that $S$ contains no zero divisors of the module. Furthermore, it is shown that associated primes exist in modules over the $S$-Noetherian rings and the major part of notions of associated prime ideals coincide over the $S$-Noetherian rings. We also extend the classical Krull's intersection theorem for $S$-Noetherian rings. Moreover, we provide a characterization of the $S$-Noetherian modules in terms of the $G$-graded $S$-Noetherian modules. |
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| DOI: | 10.3842/umzh.v77i1.7907 |