On unit elements of di_x000B_erential polynomial rings

Let R be a reversible ring which is -compatible for a derivation endomorphism on R and f (x) = a0 + a1x + + anxn be a non-zero polynomial in R[x; ]. It is proved that if there exists a non-zero polynomial g(x) = b0 + b1x + + bmxm in R[x; ] such that g(x) f (x) = c is a constant in R, then b0a0 = c and there exist non-zero elements a and r in R such that r f (x) = ac. Furthermore, we show that if b0 is a unit in R, then a1; a2; ; an are all nilpotent.