Geodesic
Homomorphisms of Rings with Involution
Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1098-1108

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The purpose of this paper is to examine the extent to which a homomorphism of a ring with involution is determined by its action on the symmetric elements of the ring. Assuming that the ring is "suitably free" of 2 × 2 matrix rings, we show that any homomorphism is uniquely determined if its image is semi-prime without nonzero central ideals. To obtain this result we first investigate automorphisms of quotients of rings with involution. 
Lanski, Charles. Homomorphisms of Rings with Involution. Canadian journal of mathematics, Tome 26 (1974) no. 5, pp. 1098-1108. doi: 10.4153/CJM-1974-102-4
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[1] 1. Amitsur, S. A., Identities in Rings with involution, Israel J. Math. 1 (1969), 63–68. Google Scholar

[2] 2. Herstein, I. N., Topics in ring theory (University of Chicago Press, Chicago, 1969). Google Scholar

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