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arXiv · 2106.09767

Cyclic and non-cyclic division algebras of finite dp-rank

Christian d'Elbée
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Abstract

Milliet asks the following question: given two prime numbers $p\neq q$, is there a division algebra of characteristic $p$ which is of dp-rank $q^2$ and of dimension $q^2$ over its center? We answer in the affirmative. We also give an example of a finite burden central division algebra over some ultraproduct of $p$-adic numbers. As a conclusion we revisit an example of Albert to prove that there exists non-cyclic division algebras of finite dp-rank.

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Christian d'Elbée. 2021-06-17. Cyclic and non-cyclic division algebras of finite dp-rank. https://arxiv.org/abs/2106.09767

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