JP Journal of Algebra, Number Theory and Applications
Volume 23, Issue 1, Pages 1 - 24
(November 2011)
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ON INTEGRAL DOMAINS WITH A UNIQUE OVERRING THAT IS INCOMPARABLE WITH THE INTEGRAL CLOSURE
David E. Dobbs and Noômen Jarboui
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Abstract: A commutative integral domain Rof finite Krull dimension rthat is neither quasilocal nor integrally closed has exactly overrings (including Rand its quotient field K) if and only if Rhas a Prüferian integral closure with a Y-shaped spectrum such that is a minimal overring of Rand there is a unique overring of Rthat is incomparable with Examples of such domains Rare given for each positive r, with a generalization to the semiquasilocal case. Characterizations are also given for the finite-dimensional domains Rwith exactly or overrings. |
Keywords and phrases: integral domain, prime ideal, overring, integral closure, Krull dimension, Prüfer domain, valuation domain, pseudo-valuation domain, irredundant intersection, minimal ring extension. |
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