Year 2010, Volume 8, Issue 8, Pages 80 - 113 2010-12-01

IDEALS AND OVERRINGS OF DIVIDED DOMAINS

Gabriel Picavet [1]

120 178

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.
affine open subset, almost pseudo-valuation domain, antesharp prime ideal, complete integral closure, conductor overring
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  • Laboratoire de Math´ematiques
  • Universit´e Blaise Pascal 63177 Aubiere Cedex
  • e-mail: Gabriel.Picavet@math.univ-bpclermont.fr
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Author: Gabriel Picavet

Bibtex @ { ieja266431, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Abdullah HARMANCI}, year = {2010}, volume = {8}, pages = {80 - 113}, doi = {}, title = {IDEALS AND OVERRINGS OF DIVIDED DOMAINS}, key = {cite}, author = {Picavet, Gabriel} }
APA Picavet, G . (2010). IDEALS AND OVERRINGS OF DIVIDED DOMAINS. International Electronic Journal of Algebra, 8 (8), 80-113. Retrieved from http://dergipark.org.tr/ieja/issue/25212/266431
MLA Picavet, G . "IDEALS AND OVERRINGS OF DIVIDED DOMAINS". International Electronic Journal of Algebra 8 (2010): 80-113 <http://dergipark.org.tr/ieja/issue/25212/266431>
Chicago Picavet, G . "IDEALS AND OVERRINGS OF DIVIDED DOMAINS". International Electronic Journal of Algebra 8 (2010): 80-113
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ISNAD Picavet, Gabriel . "IDEALS AND OVERRINGS OF DIVIDED DOMAINS". International Electronic Journal of Algebra 8 / 8 (December 2010): 80-113.