1998/01/01 by D.D. Anderson, D. D. Anderson, B.G. Kang +2 · 2 citations
Mathematics · #Rings, Modules, and Algebras #Algebraic structures and combinatorial models #Advanced Topics in Algebra
paper · doi:10.1080/00927879808826338
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.