Supertropical semirings and supervaluations
| dc.bibliographicCitation.seriesTitle | Oberwolfach Preprints (OWP) | eng |
| dc.bibliographicCitation.volume | 2010-05 | |
| dc.contributor.author | Izhakian, Zur | |
| dc.contributor.author | Knebusch, Manfred | |
| dc.contributor.author | Rowen, Louis | |
| dc.date.available | 2019-06-28T08:07:34Z | |
| dc.date.issued | 2010 | |
| dc.description.abstract | We interpret a valuation v on a ring R as a map v : R ! M into a so called bipotent semiring M (the usual max-plus setting), and then de¯ne a supervaluation ' as a suitable map into a supertropical semiring U with ghost ideal M (cf. [IR1], [IR2]) covering v via the ghost map U ! M. The set Cov(v) of all supervaluations covering v has a natural ordering which makes it a complete lattice. In the case that R is a field, hence for v a Krull valuation, we give a complete explicit description of Cov(v). The theory of supertropical semirings and supervaluations aims for an algebra fitting the needs of tropical geometry better than the usual max-plus setting. We illustrate this by giving a supertropical version of Kapranov's lemma. | eng |
| dc.description.version | publishedVersion | eng |
| dc.format | application/pdf | |
| dc.identifier.uri | https://doi.org/10.34657/3315 | |
| dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2512 | |
| dc.language.iso | eng | eng |
| dc.publisher | Oberwolfach : Mathematisches Forschungsinstitut Oberwolfach | eng |
| dc.relation.doi | https://doi.org/10.14760/OWP-2010-05 | |
| dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
| dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
| dc.subject.ddc | 510 | eng |
| dc.subject.other | Supertropical algebra | eng |
| dc.subject.other | monoids | eng |
| dc.subject.other | bipotent semirings | eng |
| dc.subject.other | valuation theory | eng |
| dc.subject.other | supervalu- ations | eng |
| dc.subject.other | transmissions | eng |
| dc.subject.other | lattices | eng |
| dc.title | Supertropical semirings and supervaluations | eng |
| dc.type | Report | eng |
| dc.type | Text | eng |
| tib.accessRights | openAccess | eng |
| wgl.contributor | MFO | eng |
| wgl.subject | Mathematik | eng |
| wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |