On graded Going down domains
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866929419026694144 |
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| author | Sahandi, Parviz Shirmohammadi, Nematollah |
| author_facet | Sahandi, Parviz Shirmohammadi, Nematollah |
| contents | Let $Γ$ be a torsionless commutative cancellative monoid and $R =\bigoplus_{α\in Γ}R_α$ be a $Γ$-graded integral domain. In this paper, we introduce the notion of graded going-down domains. Among other things, we provide an equivalent condition for graded-Prüfer domains in terms of graded going-down and graded finite-conductor domains. We also characterize graded going-down domains by means of graded divided domains. As an application, we show that the graded going-down property is stable under factor domains. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_16067 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On graded Going down domains Sahandi, Parviz Shirmohammadi, Nematollah Commutative Algebra 13A02, 13A15, 13F05 Let $Γ$ be a torsionless commutative cancellative monoid and $R =\bigoplus_{α\in Γ}R_α$ be a $Γ$-graded integral domain. In this paper, we introduce the notion of graded going-down domains. Among other things, we provide an equivalent condition for graded-Prüfer domains in terms of graded going-down and graded finite-conductor domains. We also characterize graded going-down domains by means of graded divided domains. As an application, we show that the graded going-down property is stable under factor domains. |
| title | On graded Going down domains |
| topic | Commutative Algebra 13A02, 13A15, 13F05 |
| url | https://arxiv.org/abs/2306.16067 |