An online session of the Algebra and Logic Seminar will be held on June 18, 2021 (Friday) at 1:00 p.m. (UTC +3)
A talk on

Primary decompositions of unital locally matrix algebras and Steinitz numbers

will be delivered by Bogdana Oliynik (National University of Kyiv-Mohyla Academy, Kyiv, Ukraine).

Abstract. Let F be a ground field. An F-algebra A with unit 1 is said to be a locally matrix algebra if an arbitrary finite collection of elements a₁, . . . , a_s from A lies in a subalgebra B with 1 of the algebra A, and B is isomorphic to a matrix algebra M_n(F), n ≥. We assign a Steinitz number n(A) to an arbitrary unital locally matrix algebra A. In this talk, we outline the construction of a unital locally matrix algebra of uncountable dimension that does not admit a primary de-composition. It gives negative answers to the question posed in V. M. Kurochkin, On the theory of locally simple and locally normal algebras (Russian), Mat. Sb., Nov. Ser. 22(64) (1948), no. 3, 443–454. We also show that for an arbitrary infinite Steinitz number s there exists a unital locally matrix algebra A having the Steinitz number s and being not isomorphic to a tensor product of finite dimensional matrix algebras.

This talk is based on the joint works with Oksana Bezushchak.

The seminar will be held via Zoom and everyone can join at:

https://us02web.zoom.us/j/85137375021?pwd=RE5QczdFTE1xL1R6MnI2b1lkcGczQT09

Topic: Онлайн семинар на секция “Алгебра и логика”
Time: June 18, 2021 01:00 PM Sofia
Meeting ID: 851 3737 5021
Passcode: 035647

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