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Homomorphisms of Rings with Involution

Published online by Cambridge University Press:  20 November 2018

Charles Lanski
Charles Lanski*
Affiliation:
University of Southern California, Los Angeles, California
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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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 5 , October 1974 , pp. 1098 - 1108
Copyright
Copyright © Canadian Mathematical Society 1974

References

1. Amitsur, S. A., Identities in Rings with involution, Israel J. Math. 1 (1969), 63–68.Google Scholar
2. Herstein, I. N., Topics in ring theory (University of Chicago Press, Chicago, 1969).Google Scholar