We complement two papers on supertropical valuation theory ([IKR1], [IKR2])
by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations
and transmissions between them. The supervaluations discussed have values in
totally ordered supertropical semirings, and the transmissions discussed respect the
orderings. Basics of a theory of such semirings and transmissions are developed as far as
needed.
