Farzad Padashnik - Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran
Ahmad Moussavi - Department of Pure Mathematics, Faculty of Mathematical Sciences, Tarbiat Modares University, Tehran, Iran

Let R be an associative ring with unity. (Nasr-Isfahani,4102) proved that if R be an ACCPR-ring, : RR a rigid automorphism of R and  an  -derivation of R and R satisfies the ACC on right annihilators, then R[x;, ] is an ACCPR-ring. The main result in this note is an example on the ring of a compatible ring like S such that satisfies the ACC on right annihilators but is not ACCPR-ring. Also, we show that polynomial ring S[x] is not ACCPR-ring.

ACCPR-ring, Compatible ring, Rigid ring, ACC on annihilators