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Extending Jordan Ideals and Jordan Homomorphisms of Symmetric Elements in a Ring with Involution

Published online by Cambridge University Press:  20 November 2018

Kirby C. Smith
Kirby C. Smith*
Affiliation:
University of Oklahoma, Norman, Oklahoma
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In this work, we show how the ideas in [3, pp. 6-12] can be used to give conditions under which Jordan ideals in the set of symmetric elements in an associative ring R with involution extend to associative ideals of R in a natural way. We also give conditions under which a Jordan homomorphism of the set of symmetric elements will extend to an associative homomorphism of R. Such work has been done on matrix rings with involution in [5; 6]. An abstract definition of a Jordan ring may be found in [3] as well as other background information.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 24 , Issue 1 , February 1972 , pp. 50 - 59
Copyright
Copyright © Canadian Mathematical Society 1972

References

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