1. Introduction. In a study of the commuting algebra of tensor space representations of the orthogonal group W. P. Brown encountered a class of algebras for which the existence of a unity element was equivalent to semisimplicity, but which were of interest whether or not semisimple. He gave these algebras the name generalized-total matrix algebras and proved (2) that each such algebra was characterized by three integers l, r, m and was isomorphic to the algebra of all square matrices of degree r + I + m which have zeros in the first l rows and in the last r columns.