A commutativity theorem for rings with derivations

B. Felzenszwalb, Antonio Giambruno
1982 Pacific Journal of Mathematics  
Let R be a prime ring with no nonzero nil ideals and suppose that d is a derivation of R such that d(x n ) = 0, n = n(x) ^ 1, for all xeR. 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.
doi:10.2140/pjm.1982.102.41 fatcat:igcj7xsvxfbhxb6qoq4vybiygu