ON COMPLETE INTEGRAL CLOSURE AND ARCHIMEDEAN VALUATION DOMAINS

Authors
GILMER R
Citation
R. Gilmer, ON COMPLETE INTEGRAL CLOSURE AND ARCHIMEDEAN VALUATION DOMAINS, Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics, 61, 1996, pp. 377-380
Citations number
9
Categorie Soggetti
Mathematics, General","Statistic & Probability",Mathematics,"Statistic & Probability
Journal title
Journal of the Australian Mathematical Society. Series A. Pure mathematics and statistics → ACNP
ISSN journal
02636115
Volume
61
Year of publication
1996
Part
3
Pages
377 - 380
Database
ISI
SICI code
0263-6115(1996)61:<377:OCICAA>2.0.ZU;2-0
Abstract
Suppose D is an integral domain with quotient field K and that L is an extension field of K. We show in Theorem 4 that if the complete integ ral closure of D is an intersection of Archimedean valuation domains o n K, then the complete integral closure of D in L is an intersection o f Archimedean valuation domains on L; this answers a question raised b y Gilmer and Heinzer in 1965.