2025/07/07 by Ivan D. Chipchakov, Chipchakov, Ivan D.
Mathematics · #11S15 #12F20 #12J10 #16K20 (secondary) #16K40 (primary) #FOS: Mathematics #Number Theory (math.NT) #Rings and Algebras (math.RA) #math.NT #math.RA #msc:11S15 #msc:12F20 #msc:12J10 #msc:16K20 #msc:16K40
paper · pdf · doi:10.48550/arxiv.2507.04863
10 pages, no figures: title changed, abstract and references updated, the proof of Lemma 2.1 deleted and replaced by a reference, minor improvements in the text
arxiv created 2026/07/29 · arxiv updated 2026/07/31
Let K m be an m-local field with an m-th residue field K 0, for some integer m > 0, and let K/K m be a field extension of transcendence degree 1. The paper under review shows that if K 0 is a field of finite Diophantine dimension ddim(K 0), and R is an associative locally finite-dimensional central division K-algebra, then R is a normally locally finite algebra over K, that is, every nonempty finite subset Y of R is contained in a finite-dimensional central K-subalgebra RY of R.