On the prime ideal structure of symbolic Rees algebras - Mathematics > Commutative AlgebraReport as inadecuate




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Abstract: This paper contributes to the study of the prime spectrum and dimensiontheory of symbolic Rees algebra over Noetherian domains. We first establishsome general results on the prime ideal structure of subalgebras of affinedomains, which actually arise, in the Noetherian context, as domains between adomain $A$ and $Aa^{-1}$. We then examine closely the special context ofsymbolic Rees algebras which yielded the first counter-example to theZariski-Hilbert problem. One of the results states that if $A$ is a Noetheriandomain and $p$ a maximal ideal of $A$, then the Rees algebra of $p$ inheritsthe Noetherian-like behavior of being a stably strong S-domain. We alsoinvestigate graded rings associated with symbolic Rees algebras of prime ideals$p$ such that $A {p}$ is a rank-one DVR and close with an application relatedto Hochster-s result on the coincidence of the ordinary and symbolic powers ofa prime ideal.



Author: S. Bouchiba, S. Kabbaj

Source: https://arxiv.org/







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