Complete Integral Closure and Strongly Divisorial Prime Ideals

Valentina Barucci; Stefania Gabelli; Moshe Roitman

doi:10.1081/AGB-120023967

Complete Integral Closure and Strongly Divisorial Prime Ideals

Valentina Barucci, Stefania Gabelli, Moshe Roitman

Department of Mathematics

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

Abstract

It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without prime strongly divisorial ideals is not necessarily completely integrally closed, although this property holds under some additional assumptions.

Original language	English
Pages (from-to)	5447-5465
Number of pages	19
Journal	Communications in Algebra
Volume	31
Issue number	11
DOIs	https://doi.org/10.1081/AGB-120023967
State	Published - Nov 2003

Keywords

Complete integral closure
Divisorial ideal

ASJC Scopus subject areas

Algebra and Number Theory

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10.1081/AGB-120023967

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title = "Complete Integral Closure and Strongly Divisorial Prime Ideals",

abstract = "It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without prime strongly divisorial ideals is not necessarily completely integrally closed, although this property holds under some additional assumptions.",

keywords = "Complete integral closure, Divisorial ideal",

author = "Valentina Barucci and Stefania Gabelli and Moshe Roitman",

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AU - Barucci, Valentina

AU - Gabelli, Stefania

AU - Roitman, Moshe

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N2 - It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without prime strongly divisorial ideals is not necessarily completely integrally closed, although this property holds under some additional assumptions.

AB - It is well known that a domain without proper strongly divisorial ideals is completely integrally closed. In this paper we show that a domain without prime strongly divisorial ideals is not necessarily completely integrally closed, although this property holds under some additional assumptions.

KW - Complete integral closure

KW - Divisorial ideal

UR - https://www.scopus.com/pages/publications/0242360747

U2 - 10.1081/AGB-120023967

DO - 10.1081/AGB-120023967

M3 - Article

AN - SCOPUS:0242360747

SN - 0092-7872

VL - 31

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EP - 5465

JO - Communications in Algebra

JF - Communications in Algebra

IS - 11

ER -

Complete Integral Closure and Strongly Divisorial Prime Ideals

Abstract

Keywords

ASJC Scopus subject areas

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