Yıl 2014, Cilt 16, Sayı 16, Sayfalar 99 - 114 2014-12-01

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

Ahmed Ayache [1] , David E. Dobbs [2]

154 184

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.
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
Konular
Diğer ID JA73MB53BC
Dergi Bölümü Makaleler
Yazarlar

Yazar: Ahmed Ayache

Yazar: David E. Dobbs

Bibtex @ { ieja266230, journal = {International Electronic Journal of Algebra}, issn = {1306-6048}, eissn = {1306-6048}, address = {Prof. Dr. Abdullah HARMANCI}, year = {2014}, volume = {16}, pages = {99 - 114}, doi = {10.24330/ieja.266230}, title = {CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS}, key = {cite}, author = {Dobbs, David E. and Ayache, Ahmed} }
APA Ayache, A , Dobbs, D . (2014). CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS. International Electronic Journal of Algebra, 16 (16), 99-114. DOI: 10.24330/ieja.266230
MLA Ayache, A , Dobbs, D . "CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS". International Electronic Journal of Algebra 16 (2014): 99-114 <http://dergipark.gov.tr/ieja/issue/25195/266230>
Chicago Ayache, A , Dobbs, D . "CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS". International Electronic Journal of Algebra 16 (2014): 99-114
RIS TY - JOUR T1 - CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS AU - Ahmed Ayache , David E. Dobbs Y1 - 2014 PY - 2014 N1 - doi: 10.24330/ieja.266230 DO - 10.24330/ieja.266230 T2 - International Electronic Journal of Algebra JF - Journal JO - JOR SP - 99 EP - 114 VL - 16 IS - 16 SN - 1306-6048-1306-6048 M3 - doi: 10.24330/ieja.266230 UR - http://dx.doi.org/10.24330/ieja.266230 Y2 - 2018 ER -
EndNote %0 International Electronic Journal of Algebra CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS %A Ahmed Ayache , David E. Dobbs %T CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS %D 2014 %J International Electronic Journal of Algebra %P 1306-6048-1306-6048 %V 16 %N 16 %R doi: 10.24330/ieja.266230 %U 10.24330/ieja.266230
ISNAD Ayache, Ahmed , Dobbs, David E. . "CHARACTERIZATIONS OF THE INTEGRAL DOMAINS WHOSE OVERRINGS ARE GOING-DOWN DOMAINS". International Electronic Journal of Algebra 16 / 16 (Aralık 2014): 99-114. http://dx.doi.org/10.24330/ieja.266230