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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Polynomial group laws. II
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by Zensho Nakao
Proc. Amer. Math. Soc. 80 (1980), 196-200
DOI: https://doi.org/10.1090/S0002-9939-1980-0577743-X

Abstract:

Let V be a Zariski-open (i.e., cofinite) subset of an infinite field K. Call a map $m:V \times V \to V$ separately polynomial if for each $x \in V$ the two partial maps $y \to m(x,y),y \to m(y,x)$ are polynomial. If $m:V \times V \to V$ is a separately polynomial group law, then either $V = K$ and $m(x,y) = x + y + k$ for some $k \in K$ or $V = K - \{ k\}$ and $m(x,y) = b(x - k)(y - k) + k$ for some $k \in K$ and $b \in {K^\ast } = K - \{ 0\}$.
References
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 80 (1980), 196-200
  • MSC: Primary 14L17; Secondary 20G15
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0577743-X
  • MathSciNet review: 577743