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Hilbert rings with maximal ideals of different heights and unruly Hilbert rings
Published online by Cambridge University Press: 10 March 2022
Abstract
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 characterize when $R\bowtie ^fJ$ is a Hilbert ring. As an application, we provide an example of Hilbert ring with maximal ideals of different heights. We also construct non-Noetherian Hilbert rings whose maximal ideals are all finitely generated (unruly Hilbert rings).
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- © Canadian Mathematical Society, 2022
Footnotes
This research was in part supported by a grant from IPM (No.14001300114)
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