On complete integral closure and Archimedean valuation domains

Robert Gilmer

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 integral closure of D is an intersection of Archimedean valuation domains on K, then the complete integral closure of D in L is an intersection of Archimedean valuation domains on L; this answers a question raised by Gilmer and Heinzer in 1965.

Mathematics subject classification (Amer. Math. Soc): Primary 13A18, 13B02; secondary 13B22, 13G05.