Structure of unital 3-fields
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.
2019 ◽
Vol 19
(04)
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pp. 2050061
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2016 ◽
Vol 16
(09)
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pp. 1750163
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1989 ◽
Vol 41
(1)
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pp. 14-67
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1981 ◽
Vol 24
(4)
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pp. 423-431
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