New Results On $S-r-$ideals in Commutative Rings
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866909787735719936 |
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| author | Gündüz, Abuzer Naji, Osama A. Özen, Mehmet |
| author_facet | Gündüz, Abuzer Naji, Osama A. Özen, Mehmet |
| contents | This article studies the notion of $S-r-$ideals in commutative ring $H$, where $S$ is a multiplicatively closed subset of $H$. Some basic properties of $S-r-$ideals are given. Various characterizations of $S-r-$ideals are presented. Also, $S-uz-$ring is defined and it is proved that $H$ is an $S-uz-$ring if and only if every maximal ideal disjoint from $S$ is an $S-r-$ideal provided $S$ is finite. In addition, the $S-r-$ideal concept is examined in amalgamation and trivial extension. Finally, $S-r-$ideals are studied in polynomial rings and it is investigated that when $A[x]$ is an $S-r-$ideal of $H[x].$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_19198 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | New Results On $S-r-$ideals in Commutative Rings Gündüz, Abuzer Naji, Osama A. Özen, Mehmet Commutative Algebra 13C05, 13B30, 13B25 This article studies the notion of $S-r-$ideals in commutative ring $H$, where $S$ is a multiplicatively closed subset of $H$. Some basic properties of $S-r-$ideals are given. Various characterizations of $S-r-$ideals are presented. Also, $S-uz-$ring is defined and it is proved that $H$ is an $S-uz-$ring if and only if every maximal ideal disjoint from $S$ is an $S-r-$ideal provided $S$ is finite. In addition, the $S-r-$ideal concept is examined in amalgamation and trivial extension. Finally, $S-r-$ideals are studied in polynomial rings and it is investigated that when $A[x]$ is an $S-r-$ideal of $H[x].$ |
| title | New Results On $S-r-$ideals in Commutative Rings |
| topic | Commutative Algebra 13C05, 13B30, 13B25 |
| url | https://arxiv.org/abs/2505.19198 |