Izhakian, Zur and Knebusch, Manfred and Rowen, Louis (2011) Supertropical semirings and supervaluations. JOURNAL OF PURE AND APPLIED ALGEBRA, 215 (10). pp. 2431-2463. ISSN 0022-4049,
Full text not available from this repository. (Request a copy)Abstract
We interpret a valuation nu on a ring R as a map nu : R -> M into a so-called bipotent semiring M (the usual max-plus setting), and then define a supervaluation phi as a suitable map into a supertropical semiring U with ghost ideal M (cf. Izhakian and Rowen (2010, in press) [8,9]) covering nu via the ghost map U -> M. The set Cov(nu) of all supervaluations covering nu has a natural ordering which makes it a complete lattice. In the case where R is a field, and hence for a nu Krull valuation, we give a completely explicit description of Cov(nu). 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. (C) 2011 Elsevier B.V. All rights reserved.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | COMMUTATIVE RING; ALGEBRA; VALUATIONS; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics > Professoren und akademische Räte im Ruhestand > Prof. Dr. Manfred Knebusch |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 29 May 2020 10:37 |
| Last Modified: | 29 May 2020 10:37 |
| URI: | https://pred.uni-regensburg.de/id/eprint/20151 |
Actions (login required)
 |
View Item |
