Generalized Vandermonde determinants and roots of unity of prime order
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- by R. J. Evans and I. M. Isaacs PDF
- Proc. Amer. Math. Soc. 58 (1976), 51-54 Request permission
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 $|F(\varepsilon ):F| = n$ 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
- O. H. Mitchell, Note on Determinants of Powers, Amer. J. Math. 4 (1881), no. 1-4, 341–344. MR 1505308, DOI 10.2307/2369171
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 58 (1976), 51-54
- MSC: Primary 15A15
- DOI: https://doi.org/10.1090/S0002-9939-1976-0412205-0
- MathSciNet review: 0412205