A NOTE ON $\sigma(*)$-RINGS AND THEIR EXTENSIONS
Let R be an associative ring with identity 1 6= 0, and  an endomorphism of R. We recall (¤) property on R (i.e. a.(a) 2 P(R) implies a 2 P(R) for a 2 R, where P(R) is the prime radical of R). Also recall that a ring R is said to be 2-primal if and only if the prime radical P(R) and nil radical are same, i.e. if the prime radical is a completely semiprime ideal. It can be seen that a .(¤) ring is a 2-primal ring. Let R be a ring and . an automorphism of R. Then we know that . can be extended to an automorphism of the skew polynomial ring R[x; .]. In this paper we show that if R is a Noetherian ring and . is an automorphism of R such that R is a .(¤)-ring, then R[x; .] is also a .(¤)-ring.