The next meeting of the Algebra and Logic Seminar will be held on November 22, 2024 (Friday) at 1:00 pm (UTC+2).

A talk on:

On Köthe’s normality question for locally finite-dimensional central division algebras

will be delivered by

Ivan Chipchakov, IMI – BAS.

Abstract. This talk considers Köthe’s question of whether every associative locally finite-dimensional (abbr., LFD) central division algebra R over a field K is a normally locally finite (abbr., NLF) algebra over K, that is, whether every nonempty finite subset Y of R is contained in a finite-dimensional central K-subalgebra RY of R. It shows that the answer to the posed question is negative if K is a purely transcendental extension of infinite transcendence degree over an algebraically closed field k. On the other hand, central division LFD-algebras over K turn out to be NLF in the following special cases: (i) K is a field of finite Diophantine dimension, for example, if K is a finitely-generated extension of a finite or a pseudo-algebraically closed field; (ii) K is a higher-dimensional local field with a finite last residue field.

Everybody is invited.

Algebra and Logic Department, IMI – BAS
http://www.math.bas.bg/algebra/seminarAiL/
============================== =====================