Geodesic
(Generalized) filter properties of the amalgamated algebra
Archivum mathematicum, Tome 58 (2022) no. 3, pp. 133-140 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Let $R$ and $S$ be commutative rings with unity, $f\colon R\rightarrow S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie ^fJ:=\lbrace (a,f(a)+j)\mid a\in R$ and $j\in J\rbrace $ 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.
Let $R$ and $S$ be commutative rings with unity, $f\colon R\rightarrow S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie ^fJ:=\lbrace (a,f(a)+j)\mid a\in R$ and $j\in J\rbrace $ 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.
DOI : 10.5817/AM2022-3-133
Classification : 13A15, 13C14, 13C15, 13E05, 13H10
Keywords: amalgamated algebra; Cohen-Macaulay ring; $f$-ring; generalized $f$-ring 
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Azimi, Yusof. (Generalized) filter properties of the amalgamated algebra. Archivum mathematicum, Tome 58 (2022) no. 3, pp. 133-140. doi: 10.5817/AM2022-3-133

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