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Nonstandard Arithmetic of Polynomial Rings

Published online by Cambridge University Press:  22 January 2016

Masahiro Yasumoto
Masahiro Yasumoto*
Affiliation:
Department of Mathematics Faculty of Science Nagoya University, Chikusa-ku, Nagoya 464, Japan
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Let f(X, T1,…, Tm) be a polynomial over an algebraic number field k of finite degree. In his paper [2], T. Kojima proved

THEOREM. Let K = Q. if for every m integers t1, …, tm, there exists an r ∈ K such that f(r, t1, …, tm) =), then there exists a rational function g(T1,…,Tm) over Q such that

F(g(T1,…,Tm), T1,…,T)= 0.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 105 , March 1987 , pp. 33 - 37
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1987

References

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