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Keywords:
amalgamated algebra; Cohen-Macaulay ring; $f$-ring; generalized $f$-ring
amalgamated algebra; Cohen-Macaulay ring; $f$-ring; generalized $f$-ring
Summary:
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.
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