On the corestriction ofp n -symbol

LetF be a field of characteristicp. Teichmüller 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 Teichmüller 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 .