Unital locally matrix algebras and Steinitz numbers

2019/07/26 by Bezushchak, Oksana, Oliynyk, Bogdana
#03C05 #03C60 #11E88 #FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.1907.11506

Abstract

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, that is isomorphic to a matrix algebra M_n(F), n≥ 1. To an arbitrary unital locally matrix algebra A we assign a Steinitz number n(A) and study a relationship between n(A) and A.

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