dc.contributor.author Izhakian, Zur dc.contributor.author Knebusch, Manfred dc.contributor.author Rowen, Louis dc.date.accessioned 2016-10-10T12:25:36Z dc.date.available 2016-10-10T12:25:36Z dc.date.issued 2011 dc.identifier.uri http://publications.mfo.de/handle/mfo/1240 dc.description OWLF 2010 en_US dc.description.abstract This paper is a sequel of [IKR1], where we defined supervaluations on a commutative ring $R$ and studied a dominance relation $\Phi >= v$ between supervaluations $\varphi$ and $\upsilon$ on $R$, aiming at an enrichment of the algebraic tool box for use in tropical geometry. A supervaluation $\varphi : R \rightarrow U$ is a multiplicative map from $R$ to a supertropical semiring $U$, cf. [IR1], [IR2], [IKR1], with further properties, which mean that $\varphi$ is a sort of refinement, or covering, of an m-valuation (= monoid valuation) $\upsilon:R \rightarrow M$. In the most important case, that $R$ is a ring, m-valuations constitute a mild generalization of valuations in the sense of Bourbaki [B], while $\varphi >= \upsilon$ means that $\upsilon:R \rightarrow V$ is a sort of coarsening of the supervaluation $\varphi$. If $\varphi(R)$ generates the semiring $U$, then $\varphi >= \upsilon$ if there exists a "transmission" $\alpha:U \rightarrow V$ with $\varphi=\alpha \circ \varphi$. Transmissions are multiplicative maps with further properties, cf. [IKR1, §55]. Every semiring homomorphism $\alpha:U \rightarrow V$ is a transmission, but there are others which lack additivity, and this causes a major difficulty. In the main body of the paper we study surjective transmissions via equivalence relations on supertropical semirings, often much more complicated than congruences by ideals in usual commutative algebra. en_US dc.language.iso en en_US dc.publisher Mathematisches Forschungsinstitut Oberwolfach en_US dc.relation.ispartofseries Oberwolfach Preprints;2011,07 dc.subject Supertropical algebra en_US dc.subject Supertropical semirings en_US dc.subject Bipotent semirings en_US dc.subject Valuation theory en_US dc.subject Monoid valuations en_US dc.subject Supervaluations en_US dc.subject Lattices en_US dc.title Dominance and Transmissions in Supertropical Valuation Theory en_US dc.type Preprint en_US dc.identifier.doi 10.14760/OWP-2011-07 local.scientificprogram OWLF 2010 en_US local.series.id OWP-2011-07 local.subject.msc 13 local.subject.msc 16 local.subject.msc 03 local.subject.msc 06 local.subject.msc 12 local.subject.msc 14
﻿