A Commutativity Theorem for Rings with Involution
Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1121-1143

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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).
Chacron, M. A Commutativity Theorem for Rings with Involution. Canadian journal of mathematics, Tome 30 (1978) no. 6, pp. 1121-1143. doi: 10.4153/CJM-1978-094-x
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