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Rings with Involution in which Every Trace is Nilpotent or Regular

Published online by Cambridge University Press:  20 November 2018

Susan Montgomery
Susan Montgomery*
Affiliation:
University of Southern California, Los Angelesy California
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A theorem of Marshall Osborn [15] states that a simple ring with involution of characteristic not 2 in which every non-zero symmetric element is invertible must be a division ring or the 2 × 2 matrices over a field. This result has been generalized in several directions. If R is semi-simple and every symmetric element (or skew, or trace) is invertible or nilpotent, then R must be a division ring, the 2 × 2 matrices over a field, or the direct sum of a division ring and its opposite [6; 8; 13; 16].

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 26 , Issue 1 , February 1974 , pp. 130 - 137
Copyright
Copyright © Canadian Mathematical Society 1974

References

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