Quasi-ordered rings - A uniform approach to orderings and valuations.

A quasi-order on a set S is a binary, reflexive and transitive relation on S. In [<xref>3</xref>], Fakhruddin introduced the notion of (totally) quasi-ordered fields and showed that each such field is either an ordered field or else a valued field. Hence, quasi-ordered fields are very well suited to treat ordered and valued fields simultaneously. The aim of the present paper is to prove that an analogous dichotomy holds for commutative rings with 1 as well. [ABSTRACT FROM AUTHOR]