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} having mathbb{Z}diagup 2mathbb{Z} as a residual field. One of the important technical ingredients is to intrinsically characterize the maximal ideal of mathcal{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.
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