Derivations of Rings of Infinite Matrices.

For any associative unital ringRwe investigate two rings – the ring of all infinite upper triangular matrices and the ring of all infinite matrices with the finite number of nonzero entries in each column. We describe derivations of these rings. We prove that every derivation of any of them is a sum of an inner derivation and a derivation which is induced by some derivation ofR. [ABSTRACT FROM PUBLISHER]