# valuation domain

An integral domain $R$ is a valuation domain if for all $a,b\in R$, either $a|b$ or $b|a$. Equivalently, an integral domain is a valuation domain if for any $x$ in the field of fractions of $R$, $x\notin R\implies x^{-1}\in R$.

Some properties:

Title valuation domain ValuationDomain 2013-03-22 13:47:31 2013-03-22 13:47:31 mathcam (2727) mathcam (2727) 7 mathcam (2727) Definition msc 16U10 msc 13G05 msc 13F30 PruferDomain