http://orcid.org/0000-0003-0235-9132
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ABSTRACT
A quasi-order on a set S is a binary, reflexive and transitive relation on S. In [Citation3], 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.
Acknowledgements
The results presented here are part of my PhD. I am grateful to my supervisor Salma Kuhlmann for her dedicated support in general, and for carefully reading this note in particular. Her numerous comments led to a significant improvement. I would also like to thank Tom-Lukas Kriel for helpful discussions on the subject.