Year: 2020
Type: article
Abstract: We 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.
Source: Mathematische Semesterberichte
Authors: Steven Duplij, Wend Werner
Institution: University of Münster
Language: English
Topic: Rings, Modules, and Algebras
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,760
OpenAlex ID: W278369428