Abstract
LetF be a field of characteristicp. Teichmuller proved that anyp-algebra overF of indexp n and exponentp e is similar to a tensor product with at mostp n !(p n !−1) factors of cyclicp-algebras overF of degreep e . In this note we improve Teichmuller bound for two particular types ofp-algebras. LetL be a finite separable extension ofF. IfA is a cyclicp-algebra overL of degreep e we show that Cor L/F A, the corestriction ofA, is similar to a tensor product with at most [L :F] factors of cyclicp-algebras overF of degreep e . Moreover we prove that [L :F] is the best possible bound. From this we deduce that ifA is a cyclicp-algebra overF of degreep n and exponentp e thenA is similar to a tensor product with at mostp n−e factors of cyclicp-algebras overF of degreep e .
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