On the prime spectrum of the amalgamations
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910714218676224 |
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| author | Azimi, Y. |
| author_facet | Azimi, Y. |
| contents | Let $f:R\to S$ be a ring homomorphism and $J$ be an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we will deepen the study of the prime spectrum of the amalgamations and characterize when $R\bowtie^fJ$ is a pm-ring. We also investigate the transfer of compactly packed and properly zipped property on amalgamated constructions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_16888 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the prime spectrum of the amalgamations Azimi, Y. Commutative Algebra Let $f:R\to S$ be a ring homomorphism and $J$ be an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we will deepen the study of the prime spectrum of the amalgamations and characterize when $R\bowtie^fJ$ is a pm-ring. We also investigate the transfer of compactly packed and properly zipped property on amalgamated constructions. |
| title | On the prime spectrum of the amalgamations |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2411.16888 |