Characterizations of the Integral Domains Whose Overrings Are Going-Down Domains

Ayache, Ahmed; Dobbs, David E.

doi:10.24330/ieja.266230

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Cited by 3 publications

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“…For various ring-theoretic properties P , there have been many studies of the domains all of whose overrings satisfy P [2,3,4,7]. Far fewer studies have considered domains R such that R is maximal with respect to having quotient field qf (R) and not satisfying P .…”

Section: Introductionmentioning

confidence: 99%

Maximal non-decreasing subring of its quotient field

Ayache¹

2019

GJOM

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An integral domain R is called maximal non-going down subring of its quotient field, if R is not going down, and every proper overring of R is going down. We do prove that R is a maximal non-going down subring of its quotient field if and only if R is a quasi-local domain with maximal ideal m and its integral closure R is a semi-local Prufer domain with two maximal ideals M, N such that M intersect N = m, the extension R is not going down, and R is the unique quasi-local subring of R.

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Section: Introductionmentioning

confidence: 99%