(Generalized) filter properties of the amalgamated algebra
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909397541715968 |
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| author | Azimi, Y. |
| author_facet | Azimi, Y. |
| contents | Let $R$ and $S$ be commutative rings with unity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(a,f(a)+j)\mid a\in R$ 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 determine when $R\bowtie^fJ$ is a (generalized) filter ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_13458 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | (Generalized) filter properties of the amalgamated algebra Azimi, Y. Commutative Algebra Let $R$ and $S$ be commutative rings with unity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(a,f(a)+j)\mid a\in R$ 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 determine when $R\bowtie^fJ$ is a (generalized) filter ring. |
| title | (Generalized) filter properties of the amalgamated algebra |
| topic | Commutative Algebra |
| url | https://arxiv.org/abs/2411.13458 |