1 results
On the symbol length of
$p$-algebras
- Part of
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- Journal:
- Compositio Mathematica / Volume 149 / Issue 8 / August 2013
- Published online by Cambridge University Press:
- 22 May 2013, pp. 1353-1363
- Print publication:
- August 2013
-
- Article
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- You have access
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The main result of this paper states that if
$k$ is a field of characteristic 
$p\gt 0$ and 
$A/ k$ is a central simple algebra of index 
$d= {p}^{n} $ and exponent 
${p}^{e} $, then 
$A$ is split by a purely inseparable extension of 
$k$ of the form 
$k( \sqrt[{p}^{e} ]{{a}_{i} }, i= 1, \ldots , d- 1)$. Combining this result with a theorem of Albert (for which we include a new proof), we get that any such algebra is Brauer equivalent to the tensor product of at most 
$d- 1$ cyclic algebras of degree 
${p}^{e} $. This gives a drastic improvement upon previously known upper bounds.
