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

 

Plane Frobenius sandwiches of degree $ p$


Author: D. Daigle
Journal: Proc. Amer. Math. Soc. 117 (1993), 885-889
MSC: Primary 13A35; Secondary 13F20, 14L30
MathSciNet review: 1118085
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Abstract: Let $ {\mathbf{k}}$ be a field of characteristic $ p > 0$ and $ A,R$ polynomial rings in two indeterminates over $ {\mathbf{k}}$. It is shown that, if $ {\mathbf{k}}[{R^p}] \subset A \subset R$ (strictly) then there exist $ x,y \in R$ such that $ R = {\mathbf{k}}[x,y]$ and $ A = {\mathbf{k}}[{x^p},y]$. (The case where $ {\mathbf{k}}$ is algebraically closed was proved by Ganong in 1979.) Another result is obtained in the situation where $ {R^{{p^n}}} \subseteq A \subseteq R$.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1993-1118085-2
PII: S 0002-9939(1993)1118085-2
Article copyright: © Copyright 1993 American Mathematical Society