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arXiv · 1505.04393

Structure of unital 3-fields

Steven Duplij·Wend Werner
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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 $\mathbb{Z}\diagup 2\mathbb{Z}$ 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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Steven Duplij, Wend Werner. 2015-05-17. Structure of unital 3-fields. https://doi.org/10.1007/s00591-020-00285-1

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