1. On the quotient class of non-archimedean fields
- Author
-
Bruno Dinis, Imme van den Berg, and Top, Jaap
- Subjects
Pure mathematics ,Distributivity ,General Mathematics ,010102 general mathematics ,Structure (category theory) ,Field (mathematics) ,Mathematics - Logic ,010103 numerical & computational mathematics ,Regular semigroups ,01 natural sciences ,Minkowski addition ,Convexity ,Product (mathematics) ,Algebraic operation ,Non-archimedean fields ,FOS: Mathematics ,Coset ,Cosets ,0101 mathematics ,Logic (math.LO) ,Quotient ,Mathematics - Abstract
The quotient class of a non-archimedean field is the set of cosets with respect to all of its additive convex subgroups. The algebraic operations on the quotient class are the Minkowski sum and product. We study the algebraic laws of these operations. Addition and multiplication have a common structure in terms of regular ordered semigroups. The two algebraic operations are related by an adapted distributivity law.
- Published
- 2017