On Rank- and Determinant-Preserving Mappings

We describe linear mappings of unital locally matrix algebras that preserve the normalized rank. When the ground field is the field of real or complex numbers, we also characterize linear mappings of unital locally matrix algebras that preserve the normalized determinant.

Examples of unital locally matrix algebras include:

(1) an infinite tensor product of matrix algebras over a field; and

(2) the Clifford algebra of a nondegenerate quadratic form on an infinite-dimensional vector space over an algebraically closed field of characteristic different from 2.