We complement two papers on supertropical valuation theory (, ) by providing natural examples of m-valuations (= monoid valuations), and afterwards of supervaluations and transmissions between them. These supervaluations have values in totally ordered supertropical semirings, and the transmissions discussed respect the orderings. We develop the basics of the theory of such semirings and transmissions.
Bibliographical noteFunding Information:
The research of the first author has been supported by the Oberwolfach Leibniz Fellows Programme (OWLF), Mathematisches Forschungsinstitut Oberwolfach, Germany.
This research of the second author was supported in part by the Gelbart Institute at Bar-Ilan University, the Minerva Foundation at Tel-Aviv University, the Department of Mathematics of Bar-Ilan University, and the Emmy Noether Institute at Bar-Ilan University.
This research of the first and third authors was supported by the Israel Science Foundation (grant No. 448/09).
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- Bipotent semirings
- Monoid valuations
- Ordered supertropical semirings
- Supertropical algebra
- Valuation theory
- and homomorphic equivalence relations