Author:
Duplij Steven,Werner Wend
Abstract
AbstractWe investigate fields in which addition requires three summands. These ternary fields are shown to be isomorphic to the set of invertible elements in a local ring $$\mathcal{R}$$
R
having $$\mathbb{Z}\diagup 2\mathbb{Z}$$
Z
/
2
Z
as a residual field. One of the important technical ingredients is to intrinsically characterize the maximal ideal of $$\mathcal{R}$$
R
. We include a number of illustrative examples and prove that the structure of a finite 3‑field is not connected to any binary field.
Funder
Westfälische Wilhelms-Universität Münster
Publisher
Springer Science and Business Media LLC
Reference20 articles.
1. Bagger, J. and N. Lambert [2008]. Gauge symmetry and supersymmetry of multiple M2-branes. Phys. Rev. D77, 065008.
2. Bohle, D. and W. Werner [2015]. A K-theoretic approach to the classification of symmetric spaces. J. Pure and App. Algebra 219 (10), 4295–4321.
3. Grundlehren der mathematischen Wissenschaften;S Bosch,1984
4. Celakoski, N. [1977]. On (F,G)-rings. God. Zb., Mat. Fak. Univ. Kiril Metodij Skopje 28, 5–15.
5. Cambridge Tracts in Mathematics;C-H Chu,2012