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.
Bibliographical noteThis 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
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.
- tropical algebra
- tropical categories
- tropical geometry
- valued monoids