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A Commutativity Theorem for Rings with Involution

Published online by Cambridge University Press:  20 November 2018

M. Chacron
M. Chacron*
Affiliation:
Carl eton University, Ottawa, Ontario
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A ring with involution R is an associative ring endowed with an antiautomorphism * of period 2. One of the first commutativity results for rings with * is a theorem of S. Montgomery asserting that if R is a prime ring, in which every symmetric element s = s* is of the form s — sn(s) (n(s) ≧ 2), then either R is commutative or R is the 2 X 2 matrices over a field, which is a nice generalization of a well-known theorem of N. Jacobson on rings all of whose elements x = xn(x).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 6 , 01 December 1978 , pp. 1121 - 1143
Copyright
Copyright © Canadian Mathematical Society 1978

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