Anti-archimedean rings and power series rings

Abstract

We define an integral domain D to be anti-Archimedean if . For example, a valuation domain or SFT Prüfer domain is anti-Archimedean if and only if it has no height-one prime ideals. A number of constructions and stability results for anti-Archimedean domains are given. We show that D is anti-Archimedean is quasilocal and in this case is actually an n-dimensional regular local ring. We also show that if D is an SFT Prüfer domain, then is a Krull domain for any set of indeterminates {X α}.