Let R be a ring with an automorphism 17. An ideal [ of R is (

-ideal of R if

(I).= I. A proper ideal P of R is (

-prime ideal of R if P is a

-ideal of R and for

-ideals I and J of R, IJ

P implies that I

P or J

P. A proper ideal Q of R is

-semiprime ideal of Q if Q is a

-ideal and for a

-ideal I of R, I

Q implies that I

Q. The

-prime radical is defined by the intersection of all

-prime ideals of R and is denoted by P

(R). In this paper, the following results are obtained: (1) For a principal ideal domain R, P

(R) is the smallest

-semiprime ideal of R; (2) For any ring R with an automorphism

and for a skew Laurent polynomial ring R[x, x

;

], the prime radical of R[x, x

;

] is equal to P

(R)[x, x

;

].