Vol. 83, No. 2, 1979

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Commutation with skew elements in rings with involution

Charles Philip Lanski

Vol. 83 (1979), No. 2, 393–399

This paper describes the structure of additive subgroups and of subrings which are invariant under Lie commutation with higher commutators of the skew-symmetric elements in 2-torsion free rings with involution. Except for cases arising when the subring is central, or when the ring satisfies a polynomial identity of small degree, the invariant subring must contain an ideal of the ring. With the same exceptions, the invariant subgroup must contain either the derived Lie ring of the set of skew-symmetric elements in some ideal, or the Lie product of the set of skew-symmetric elements in the ideal with the set of symmetric elements in the ideal. Furthermore, the appropriate one of these Lie products is not Lie solvable.

Mathematical Subject Classification
Primary: 16A68, 16A68
Secondary: 16A70
Received: 4 December 1978
Revised: 5 March 1979
Published: 1 August 1979
Charles Philip Lanski