Vol. 102, No. 1, 1982

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A commutativity theorem for rings with derivations

B. Felzenszwalb and Antonio Giambruno

Vol. 102 (1982), No. 1, 41–45
Abstract

Let R be a prime ring with no nonzero nil ideals and suppose that d is a derivation of R such that d(xn) = 0, n = n(x) 1, for all x R. It is shown that either d = 0 or R is an infinite commutative domain of characteristic p0 and pn(x) if d(x)0.

Mathematical Subject Classification
Primary: 16A12, 16A12
Secondary: 16A70
Milestones
Received: 1 July 1981
Published: 1 September 1982
Authors
B. Felzenszwalb
Antonio Giambruno