Unital locally matrix algebras and Steinitz numbers.

An F -algebra A with unit 1 is said to be a locally matrix algebra if an arbitrary finite collection of elements a 1 , ... , 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 s t (A) and study a relationship between s t (A) and A. [ABSTRACT FROM AUTHOR]