ANTI-ARCHIMEDEAN RINGS AND POWER SERIES RINGS

Abstract

We define an integral domain D to be anti-Archimedean if boolean AND(n=1)(infinity) a(n)D not equal 0 for each 0 not equal a epsilon D. For example, a valuation domain or SFT Prufer 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 double left right arrow D[X-l,...,X-n](D-(0)) is quasilocal and in this case D[X-l,...,X-n](D-(0)) is actually an n-dimensional regular local ring. We also show that ii D is an SFT Prufer domain, then D[{X-alpha}](lD-(0)) is a Krull domain for any set of indeterminates {X-alpha}.