Hilbert rings with maximal ideals of different heights and unruly Hilbert rings
Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 196-203
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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).
Mots-clés :
Amalgamated algebra, Hilbert ring, pullback, trivial extension
Azimi, Y. Hilbert rings with maximal ideals of different heights and unruly Hilbert rings. Canadian mathematical bulletin, Tome 66 (2023) no. 1, pp. 196-203. doi: 10.4153/S0008439522000200
@article{10_4153_S0008439522000200,
author = {Azimi, Y.},
title = {Hilbert rings with maximal ideals of different heights and unruly {Hilbert} rings},
journal = {Canadian mathematical bulletin},
pages = {196--203},
year = {2023},
volume = {66},
number = {1},
doi = {10.4153/S0008439522000200},
url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000200/}
}
TY - JOUR AU - Azimi, Y. TI - Hilbert rings with maximal ideals of different heights and unruly Hilbert rings JO - Canadian mathematical bulletin PY - 2023 SP - 196 EP - 203 VL - 66 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000200/ DO - 10.4153/S0008439522000200 ID - 10_4153_S0008439522000200 ER -
%0 Journal Article %A Azimi, Y. %T Hilbert rings with maximal ideals of different heights and unruly Hilbert rings %J Canadian mathematical bulletin %D 2023 %P 196-203 %V 66 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4153/S0008439522000200/ %R 10.4153/S0008439522000200 %F 10_4153_S0008439522000200
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