A commutativity theorem for rings with derivations

B. Felzenszwalb and Antonio Giambruno

Vol. 102 (1982), No. 1, 41–45

DOI: 10.2140/pjm.1982.102.41

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 p≠0 and p∖n(x) if d(x)≠0.

Mathematical Subject Classification

Primary: 16A12, 16A12

Secondary: 16A70

Milestones

Received: 1 July 1981

Published: 1 September 1982