An arithmetic obstruction to division algebra decomposability

Brussel, Eric

doi:10.1090/S0002-9939-00-05296-5

An arithmetic obstruction to division algebra decomposability
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by Eric S. Brussel PDF

Proc. Amer. Math. Soc. 128 (2000), 2281-2285 Request permission

Abstract:

This paper presents an indecomposable finite-dimensional division algebra of $p$-power index that decomposes over a prime-to-$p$ degree field extension, obtained by adjoining $p$-th roots of unity to the base. This shows that the theory of decomposability has an arithmetic aspect.

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