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Invariant Subgroups in Rings with Involution

Published online by Cambridge University Press:  20 November 2018

Susan Montgomery
Susan Montgomery*
Affiliation:
University of Southern California, Los Angeles, California
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Let R be a ring with involution*. In this paper, we study additive subgroups A of R which are invariant under all mappings of the form ϕx : a → xax*. That is, xAx* ⊆ A for all x ∈ R. Obvious examples of such subgroups A are ideals of R, the set of symmetric elements, and the set of skew-symmetric elements. We will prove that when R is *-prime, these examples are essentially the only ones.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 350 - 357
Copyright
Copyright © Canadian Mathematical Society 1978

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