IDEALS AND OVERRINGS OF DIVIDED DOMAINS

Yıl 2010, Cilt: 8 Sayı: 8, 80 - 113, 01.12.2010

Gabriel Picavet

Öz

New properties of divided domains R are established by looking at multiplicatively closed subsets associated to ring morphisms. Let I be an ideal of R. We exhibit primary ideals, like I√I and In if I is primary. We show that Ass(I) = V(I) ∩ Spec(RMax(Ass(I))). Moreover, the image of the maximal spectrum of (I : I) is contained in Ass(I). We show that certain intersections of ideals are primary ideals. Goldman prime ideals are prime gideals. The characterization of maximal flat epimorphic subextensions gives as a result that R is a valuation subring of Pr¨ufer hulls. We characterize Fontana-Houston divided Ω-domains, divided APVDs and divided PPC-domains.

Anahtar Kelimeler

affine open subset, almost pseudo-valuation domain, antesharp prime ideal, complete integral closure, conductor overring

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