ON P-DERIVATIONS AND P-JORDAN DERIVATIONS OF A RING

Abstract

In this paper, we generalize ordinary derivation and Jordan derivation of a ring to the concepts of P-derivation and P-Jordan derivation of a ring respectively.  Some properties, e.g. the composition of P-derivations and P-Jordan derivations, are given.  Moreover, it proved that if R/P (R) is 2-torsion free for a ring R and its prime radicalP(R), P-Jordan derivations of R are P-derivations.  More mainly, some conclusions on the commutativity of R/I and R/P(R) are obtained via P-derivations and P-Jordan derivations, for a prime ideal I of R.