Categories of Layered Semirings

Zur Izhakian, Manfred Knebusch, Louis Rowen

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 languageEnglish
Pages (from-to)1807-1836
Number of pages30
JournalCommunications in Algebra
Issue number5
Early online date27 Feb 2015
Publication statusPublished - 4 May 2015

Bibliographical note

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.


  • tropical algebra
  • tropical categories
  • tropical geometry
  • tropicalization
  • vaulations
  • valued monoids


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