Submission date: 17 June 2021

Abstract:

Milliet asks the following question: given two prime numbers p ≠ 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.

Mathematics Subject Classification: 03C45, 11D57, 11D88, 12J10, 16K20

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Full text arXiv 2106.09767: pdf, ps.