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On algebraic central division algebras over Henselian fields of finite absolute Brauer p-dimensions and residually arithmetic type

2022/07/05 by Ivan D. Chipchakov, Chipchakov, Ivan D.
Mathematics · #12E15 #12F10 (secondary) #12G05 #12J10 (primary) #16K40 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:12E15 #msc:12F10 #msc:12G05 #msc:12J10 #msc:16K40

paper · pdf · doi:10.48550/arxiv.2207.02154

35 pages, LaTeX: A number of improvements in the text and in the organization of its presentation; references updated

arxiv created 2026/07/29 · arxiv updated 2026/07/31

Abstract

Let (K, v) be a Henselian field with a residue field \widehat K and value group v(K), and let ℙ be the set of prime numbers. This paper finds conditions on K, v(K) and \widehat K under which every algebraic associative central division K-algebra R contains a central K-subalgebra \widetilde R decomposable into a tensor product of central K-subalgebras R p, p ∈ ℙ, of finite p-primary dimensions [R p\colon K], such that each finite-dimensional K-subalgebra Δ of R is isomorphic to a K-subalgebra \widetilde Δ of \widetilde R.

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