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; ].

sigma-semiprime ring;sigma-prime ring;sigma-prime radical;skew Laurent polynomial rin;

English