Address: Department of Mathematics, University of Tabriz, Tabriz, Iran and School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box 19395-5746, Tehran, Iran
E-mail: u.azimi@tabrizu.ac.ir
Abstract: 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.
AMSclassification: primary 13A15; secondary 13C14, 13C15, 13E05, 13H10.
Keywords: amalgamated algebra, Cohen-Macaulay ring, f-ring, generalized f-ring.
DOI: 10.5817/AM2022-3-133