Vol. 44, No. 2, 1973

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On the relationship of a ring and the subring generated by its symmetric elements

Charles Philip Lanski

Vol. 44 (1973), No. 2, 581–592

Let R be a ring with involution, and S the subring generated by the symmetric elements of R. By placing various conditions on the elements of S, it is shown that the same conditions are forced on R. For example, if S is nil or algebraic, then so is R. Also, if R is assumed to be simple, prime, or semi-prime, then S satisfies the same property. Lastly, each of these three conditions on S implies the same property for R, modulo a nilpotent ideal of R.

Mathematical Subject Classification
Primary: 16A28
Received: 11 October 1971
Revised: 28 February 1972
Published: 1 February 1973
Charles Philip Lanski