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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Polynomial group laws. II


Author: Zensho Nakao
Journal: Proc. Amer. Math. Soc. 80 (1980), 196-200
MSC: Primary 14L17; Secondary 20G15
MathSciNet review: 577743
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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\} $.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0577743-X
PII: S 0002-9939(1980)0577743-X
Keywords: Separately polynomial group laws
Article copyright: © Copyright 1980 American Mathematical Society