Vol. 49, No. 1, 1973

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ISSN: 0030-8730
Homomorphisms of matrix rings into matrix rings

Amos A. Kovacs

Vol. 49 (1973), No. 1, 161–170

Let V n(Rn) be the universal ring with respect to embeddings of the matrix ring Rn into n × n matrix rings over commutative rings. A construction and a representation is given for this ring. As a main tool in the construction, it is proved that every R homomorphism of Rn,R a commutative ring, is the restriction of an inner automorphism of Un, for some U R. Using this, a necessary and sufficient condition for n2 matrices in Rn to be matrix units is given.

Mathematical Subject Classification
Primary: 16A42
Received: 5 July 1972
Published: 1 November 1973
Amos A. Kovacs