Nonnil-S-Laskerian Rings
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912768720896000 |
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| author | Singh, Tushar Ansari, Ajim Uddin Kumar, Shiv Datt |
| author_facet | Singh, Tushar Ansari, Ajim Uddin Kumar, Shiv Datt |
| contents | In this paper, we introduce the concept of nonnil-S-Laskerian rings, which generalize both nonnil-Laskerian rings and S-Laskerian rings. A ring R is said to be nonnil-S-Laskerian if every nonnil ideal I (disjoint from S) of R is S-decomposable. As a main result, we prove that the class of nonnil-S-Noetherian rings belongs to the class of nonnil-S-Laskerian rings. Also, we prove that a nonnil-S-Laskerian ring has S-Noetherian spectrum under a mild condition. Among other results, we prove that if the power series ring R[[X]] is nonnil-S-Laskerian with S-decomposable nilradical, then R is S-laskerian and satisfies the S-SFT property. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_14519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonnil-S-Laskerian Rings Singh, Tushar Ansari, Ajim Uddin Kumar, Shiv Datt Commutative Algebra 13E05, 13E99, 13F25, 16N40 In this paper, we introduce the concept of nonnil-S-Laskerian rings, which generalize both nonnil-Laskerian rings and S-Laskerian rings. A ring R is said to be nonnil-S-Laskerian if every nonnil ideal I (disjoint from S) of R is S-decomposable. As a main result, we prove that the class of nonnil-S-Noetherian rings belongs to the class of nonnil-S-Laskerian rings. Also, we prove that a nonnil-S-Laskerian ring has S-Noetherian spectrum under a mild condition. Among other results, we prove that if the power series ring R[[X]] is nonnil-S-Laskerian with S-decomposable nilradical, then R is S-laskerian and satisfies the S-SFT property. |
| title | Nonnil-S-Laskerian Rings |
| topic | Commutative Algebra 13E05, 13E99, 13F25, 16N40 |
| url | https://arxiv.org/abs/2512.14519 |