Journal Name:
- European Journal of Pure and Applied Mathematics
| Author Name | University of Author |
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Abstract (2. Language):
Let R be an associative ring with identity 1 = 0, and a an endomorphism of R. We recall a(*) property on R (i.e. aa(a) e P(R) implies a e P(R) for a e 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 P(R) and the set of nilpotent elements of R coincide, if and only if the prime radical is a completely semiprime ideal. It can be seen that a a(*)-ring is a 2-primal ring.
Let R be a ring and a an automorphism of R. Then we know that a can be extended to an automorphism (say a) of the skew-Laurent ring R[x, x-1; a]. In this paper we show that if R is a Noetherian ring and a is an automorphism of R such that R is a a(*)-ring, then R[x,x-1; a] is a a(*)-ring. We also prove a similar result for the general Ore extension R[x; a, 5], where a is an automorphism of R and 5 a a-derivation of R.
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