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2017 The prime spectrum and dimension of ideal transform algebras
Kamal Bahmanpour
Rocky Mountain J. Math. 47(5): 1415-1426 (2017). DOI: 10.1216/RMJ-2017-47-5-1415

Abstract

Let $(R,\mathfrak{m} )$ be a commutative Noetherian local ring of dimension $d\geq 1$, and let $I$ be a non-nilpotent ideal of $R$ such that the ideal transform functor $D_I(-)$ is exact. In this paper, it is shown that the finitely generated flat $R$-algebra $D_I(R)$ is a Noetherian ring of dimension $n=\dim R/\Gamma _I(R)-1$. Also, it is shown that, under Zariski topologies on the sets $Spec D_I(R)$ and $Spec R/\Gamma _I(R)$, there is a homeomorphism of topological spaces: \[ \widetilde {\eta ^*}:Spec D_I(R)\longrightarrow Spec R/\Gamma _I(R)\setminus V((I+\Gamma _I(R))/\Gamma _I(R)). \]

Citation

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Kamal Bahmanpour. "The prime spectrum and dimension of ideal transform algebras." Rocky Mountain J. Math. 47 (5) 1415 - 1426, 2017. https://doi.org/10.1216/RMJ-2017-47-5-1415

Information

Published: 2017
First available in Project Euclid: 22 September 2017

zbMATH: 06790020
MathSciNet: MR3705759
Digital Object Identifier: 10.1216/RMJ-2017-47-5-1415

Subjects:
Primary: 13D45 , 13E05 , 14B15

Keywords: cohomological dimension , ideal transform functor , local cohomology , Noetherian ring , Zariski topology

Rights: Copyright © 2017 Rocky Mountain Mathematics Consortium

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Vol.47 • No. 5 • 2017
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