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Generalized Vandermonde determinants and roots of unity of prime order

Authors: R. J. Evans and I. M. Isaacs
Journal: Proc. Amer. Math. Soc. 58 (1976), 51-54
MSC: Primary 15A15
MathSciNet review: 0412205
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Abstract: Easy proofs are given for two theorems of O. H. Mitchell about a type of generalized Vandermonde determinant. One of these results is then used to prove that if $ \vert F(\varepsilon ):F\vert = n$ where $ F$ is a field of characteristic zero and $ \varepsilon $ is a root of unity of prime order, then every set of $ n$ powers of $ \varepsilon $ forms an $ F$-basis for $ F(\varepsilon )$.

References [Enhancements On Off] (What's this?)

  • [1] O. H. Mitchell, Note on determinants of powers, Amer. J. Math. 4 (1881), 341-344. MR 1505308

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Keywords: Vandermonde determinant, roots of unity
Article copyright: © Copyright 1976 American Mathematical Society

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