Let R be a prime ring with d a left R{algebraic derivation. All possible left R{algebraic relations of d are described by a speci¯c ideal of the skew polynomial ring R[x; d]. Moreover, the prime radical and the minimal prime ideals over such ideal are also determined. As an application to the main theorem, the nilpotent case is completely obtained.
Subjects
Prime ring
Martindale quotient ring
skew polynomial ring
algebraic derivation
central generator.
Publisher
Department of Mathematics, National Taiwan University
