IDEALS AND OVERRINGS OF DIVIDED DOMAINS

Authors : Gabriel Picavet

Pages : 80-113

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Publication Date : 2010-12-01

Article Type : Research Paper

Abstract :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 Assinsert ignore into journalissuearticles values(I); = Vinsert ignore into journalissuearticles values(I); ∩ Specinsert ignore into journalissuearticles values(RMaxinsert ignore into journalissuearticles values(Assinsert ignore into journalissuearticles values(I);););. Moreover, the image of the maximal spectrum of insert ignore into journalissuearticles values(I : I); is contained in Assinsert ignore into journalissuearticles values(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.
Keywords : affine open subset, almost pseudo valuation domain, antesharp prime ideal, complete integral closure, conductor overring