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Galois structure on integral valued polynomials (1511.01295v2)

Published 4 Nov 2015 in math.NT and math.RA

Abstract: We characterize finite Galois extensions $K$ of the field of rational numbers in terms of the rings ${\rm Int}{\mathbb{Q}}(\mathcal O_K)$, recently introduced by Loper and Werner, consisting of those polynomials which have coefficients in $\mathbb{Q}$ and such that $f(\mathcal O_K)$ is contained in $\mathcal O_K$. We also address the problem of constructing a basis for ${\rm Int}{\mathbb{Q}}(\mathcal O_K)$ as a $\mathbb{Z}$-module.

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