Ahmed Ayache, David E. Dobbs

2215

CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS

Let R be a (commutative integral) domain with quotient K; let R0 be the integral closure of R (in K). Then each overring of R (inside K) is a going-down domain if and only if R0 is a locally pseudo-valuation domain, T ⊆T0 satisfies going-down for every overring T of R, and tr. deg[VR0 (M)/M(R0)M :R0/M] ≤ 1 for every maximal ideal M of R0 (where VR0 (M) denotes the valuation domain that is canonically associated to the pseudo-valuation domain (R0)M). Additional equivalences are given in case R is locally finitedimensional. Applications include the case where R is integrally closed or R is not a Jaffard domain or R[X] is catenarian.
Keywords:

Going-down domain, overring, treed domain pseudo-valuation domain, valuation domain,

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  • P.O. Box 12460, Sana’a, Yemen e-mail: aaayache@yahoo.com David E. Dobbs
  • Department of Mathematics University of Tennessee Knoxville, TN 37996-1320, U.S.A. e-mail: ddobbs1@utk.edu
International Electronic Journal of Algebra-Cover
  • ISSN: 1306-6048
  • Yayın Aralığı: Yılda 2 Sayı
  • Başlangıç: 2007
  • Yayıncı: Abdullah HARMANCI
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