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The generic division rings

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Abstract

LetA=k (X 1, X2..., Xm) be the division ring generated by genericn×n matrices over a fieldk; thenA is not a crossed product in the following cases: (i) there exists a primeq such thatq 3ℛn;(ii)[k:Q]=m, whereQ is the field of rationals, then if eitherq 3ℛn for someq for whichq-1ℛm, orq 2/nn for some other prime; (iii)k=Z p r a finite field ofp r elements and eitherq 3ℛn for sameqℛp r-1 orq 2ℛn for some other primes. Other cases are also considered.

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References

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Authors and Affiliations

  1. Institute of Mathematics, The Hebrew University of Jerusalem, Jerusalem, Israel

    S. A. Amitsur

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  1. S. A. Amitsur
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Amitsur, S.A. The generic division rings. Israel J. Math. 17, 241–247 (1974). https://doi.org/10.1007/BF02756873

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  • DOI: https://doi.org/10.1007/BF02756873

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