Monoid Valuations and Value Ordered Supervaluations
Zur Izhakian, Manfred Knebusch, Louis Rowen
TL;DR
This paper introduces natural examples of monoid valuations within supertropical valuation theory, expanding the framework to include ordered supertropical semirings and their transmissions, building on prior foundational work.
Contribution
It provides new examples of m-valuations and develops the basic theory of ordered supertropical semirings and their transmissions, complementing previous research.
Findings
Constructed natural examples of m-valuations
Developed foundational theory of ordered supertropical semirings
Analyzed transmissions respecting orderings
Abstract
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.
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