Abstract
We generalize the constructions of layered domains† to layered semirings, in order to enrich the structure, and in particular to provide finite examples for applications in arithmetic. The layered category theory is extended accordingly, to cover noncancellative monoids, which are examined in their own right.
| Original language | English |
|---|---|
| Pages (from-to) | 1807-1836 |
| Number of pages | 30 |
| Journal | Communications in Algebra |
| Volume | 43 |
| Issue number | 5 |
| DOIs | |
| State | Published - 4 May 2015 |
Bibliographical note
Publisher Copyright:© 2015, Taylor & Francis Group, LLC.
Funding
This research of the first and third authors is supported by the Israel Science Foundation (grant No. 448/09). This research of the first author has been supported by the Oberwolfach Leibniz Fellows Programme (OWLF), Mathematisches Forschungsinstitut Oberwolfach, Germany. The second author was supported in part by the Gelbart Institute at Bar-Ilan University, the Minerva Foundation at Tel-Aviv University, the Mathematics Dept. of Bar-Ilan University, and the Emmy Noether Institute.
| Funders | Funder number |
|---|---|
| Emmy Noether Research Institute for Mathematics | |
| Gelbart Institute at Bar-Ilan University | |
| Mathematics Dept. of Bar-Ilan University | |
| Mathematisches Forschungsinstitut Oberwolfach | |
| Oberwolfach Leibniz Fellows Programme | |
| Tel Aviv University | |
| Israel Science Foundation | 448/09 |
Keywords
- Tropical algebra
- Tropical categories
- Tropical geometry
- Tropicalization
- Valuations
- Valued monoids
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