Abstract
We give a geometric method of classifying algebras A n,K , n-dimensional over a field K, with a cyclic extension of degree n. Algebras A n,K without zero divisors satisfying some conditions are classified. In particular, we determine all n-dimensional division algebras over a finite field F q when n is prime and q is large enough.
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This research was supported in part by a grant from the M U R S T (40 % funds).
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Menichetti, G. n-Dimensional algebras over a field with a cyclic extension of degree n . Geom Dedicata 63, 69–94 (1996). https://doi.org/10.1007/BF00181186
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DOI: https://doi.org/10.1007/BF00181186