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 |
| Externally published | Yes |
Keywords
- Tropical algebra
- Tropical categories
- Tropical geometry
- Tropicalization
- Valuations
- Valued monoids