Geodesic
Unitaries in Simple Artinian Rings
Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 542-557

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a 2-torsion free simple artinian ring with involution*. The element u of R is said to be unitary if u is invertible with inverse u*. In this paper we shall be concerned with the subalgebras W of R over its centre Z such that uWu* ⊆ W, for all unitaries u of R. We prove that if R has rank superior to 1 over a division ring D containing more than 5 elements and if R is not 4-dimensional then any such subalgebra W must be one of the trivial subalgebras 0, Z or R, under one of the following extra finiteness assumptions: W contains inverses, W satisfies a polynomial identity, the ground division ring D is algebraic, the involution is a conjugate-transpose involution such that D equipped with the induced involution is generated by unitaries. 
Chacron, M. Unitaries in Simple Artinian Rings. Canadian journal of mathematics, Tome 31 (1979) no. 3, pp. 542-557. doi: 10.4153/CJM-1979-057-1
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