Some remarks on Prüfer rings with zero-divisors
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866929296292970496 |
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| author | Campanini, Federico Finocchiaro, Carmelo Antonio |
| author_facet | Campanini, Federico Finocchiaro, Carmelo Antonio |
| contents | Let $A$ be the fiber product $R\times_TB$, where $B\to T$ is a surjective ring homomorphism with regular kernel and $R\subseteq T$ is a ring extension where $T$ is an overring of $R$. In this paper we provide a characterization of when $A$ has distinguished Prüfer-like properties and new constructions of Prüfer rings with zero-divisors. Furthermore we give examples of homomorphic images of Prüfer rings that are Prüfer without assuming that the kernel of the surjection is regular. Finally we provide some remarks on the ideal theory of pre-Prüfer rings. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_20220 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some remarks on Prüfer rings with zero-divisors Campanini, Federico Finocchiaro, Carmelo Antonio Commutative Algebra Let $A$ be the fiber product $R\times_TB$, where $B\to T$ is a surjective ring homomorphism with regular kernel and $R\subseteq T$ is a ring extension where $T$ is an overring of $R$. In this paper we provide a characterization of when $A$ has distinguished Prüfer-like properties and new constructions of Prüfer rings with zero-divisors. Furthermore we give examples of homomorphic images of Prüfer rings that are Prüfer without assuming that the kernel of the surjection is regular. Finally we provide some remarks on the ideal theory of pre-Prüfer rings. |
| title | Some remarks on Prüfer rings with zero-divisors |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2403.20220 |