On the prime spectrum of an integral domain with finite spectral semistar operations

A. Mimouni; Zhongming Tang

doi:10.1142/s1005386711000848

On the prime spectrum of an integral domain with finite spectral semistar operations

A. Mimouni^*, Zhongming Tang

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

Abstract

In this paper, we investigate the prime spectrum of an integral domain R with a finite number of spectral semistar operations. This will be done by seeking for a possible link between the cardinality of the set SpSS(R) of all spectral semistar operations on R and its Krull dimension. In particular, we prove that if |SpSS(R)|=n+dimR, then 2^|Max(R)|≤ n+1. This leads us to give a complete description for the spectrum of a domain R such that |SpSS(R)|=n+dimR for 1 ≤ n ≤ 5.

Original language	English
Pages (from-to)	965-972
Number of pages	8
Journal	Algebra Colloquium
Volume	18
Issue number	SPEC. ISSUE 1
DOIs	https://doi.org/10.1142/s1005386711000848
State	Published - Dec 2011

Keywords

Krull dimension
Y-graph spectrum
semistar operation
spectral semistar operation

ASJC Scopus subject areas

Algebra and Number Theory
Applied Mathematics

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10.1142/s1005386711000848

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abstract = "In this paper, we investigate the prime spectrum of an integral domain R with a finite number of spectral semistar operations. This will be done by seeking for a possible link between the cardinality of the set SpSS(R) of all spectral semistar operations on R and its Krull dimension. In particular, we prove that if |SpSS(R)|=n+dimR, then 2|Max(R)|≤ n+1. This leads us to give a complete description for the spectrum of a domain R such that |SpSS(R)|=n+dimR for 1 ≤ n ≤ 5.",

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AU - Mimouni, A.

AU - Tang, Zhongming

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N2 - In this paper, we investigate the prime spectrum of an integral domain R with a finite number of spectral semistar operations. This will be done by seeking for a possible link between the cardinality of the set SpSS(R) of all spectral semistar operations on R and its Krull dimension. In particular, we prove that if |SpSS(R)|=n+dimR, then 2|Max(R)|≤ n+1. This leads us to give a complete description for the spectrum of a domain R such that |SpSS(R)|=n+dimR for 1 ≤ n ≤ 5.

AB - In this paper, we investigate the prime spectrum of an integral domain R with a finite number of spectral semistar operations. This will be done by seeking for a possible link between the cardinality of the set SpSS(R) of all spectral semistar operations on R and its Krull dimension. In particular, we prove that if |SpSS(R)|=n+dimR, then 2|Max(R)|≤ n+1. This leads us to give a complete description for the spectrum of a domain R such that |SpSS(R)|=n+dimR for 1 ≤ n ≤ 5.

KW - Krull dimension

KW - Y-graph spectrum

KW - semistar operation

KW - spectral semistar operation

UR - https://www.scopus.com/pages/publications/81255141067

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DO - 10.1142/s1005386711000848

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JO - Algebra Colloquium

JF - Algebra Colloquium

IS - SPEC. ISSUE 1

ER -

On the prime spectrum of an integral domain with finite spectral semistar operations

Abstract

Keywords

ASJC Scopus subject areas

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