PRIME IDEALS SURVIVING IN COMPLETE INTEGRAL CLOSURES

Authors
DOBBS DE
Citation
De. Dobbs, PRIME IDEALS SURVIVING IN COMPLETE INTEGRAL CLOSURES, Archiv der Mathematik, 69(6), 1997, pp. 465-469
Citations number
17
Journal title
Archiv der Mathematik → ACNP
ISSN journal
0003889X
Volume
69
Issue
6
Year of publication
1997
Pages
465 - 469
Database
ISI
SICI code
0003-889X(1997)69:6<465:PISICI>2.0.ZU;2-Q
Abstract
It is proved that if R is an Archimedean domain such that each finitel y generated proper ideal of R is contained in the radical of a proper principal ideal, then each prime ideal of R survives in the complete i ntegral closure of R. One consequence is a new proof that each Archime dean QR-domain is completely integrally closed.