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dc.contributor.authorIzhakian, Zur
dc.contributor.authorKnebusch, Manfred
dc.contributor.authorRowen, Louis
dc.date.accessioned2016-10-10T12:25:36Z
dc.date.available2016-10-10T12:25:36Z
dc.date.issued2011
dc.identifier.urihttp://publications.mfo.de/handle/mfo/1240
dc.descriptionOWLF 2010en_US
dc.description.abstractThis 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.isoenen_US
dc.publisherMathematisches Forschungsinstitut Oberwolfachen_US
dc.relation.ispartofseriesOberwolfach Preprints;2011,07
dc.subjectSupertropical algebraen_US
dc.subjectSupertropical semiringsen_US
dc.subjectBipotent semiringsen_US
dc.subjectValuation theoryen_US
dc.subjectMonoid valuationsen_US
dc.subjectSupervaluationsen_US
dc.subjectLatticesen_US
dc.titleDominance and Transmissions in Supertropical Valuation Theoryen_US
dc.typePreprinten_US
dc.identifier.doi10.14760/OWP-2011-07
local.scientificprogramOWLF 2010en_US
local.series.idOWP-2011-07
local.subject.msc13
local.subject.msc16
local.subject.msc03
local.subject.msc06
local.subject.msc12
local.subject.msc14


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