Prime Radicals of Skew Laurent Polynomial Rings
نویسنده
چکیده
Let R be a ring with an automorphism σ. An ideal I of R is σ-ideal of R if σ(I) = I. A proper ideal P of R is σ-prime ideal of R if P is a σ-ideal of R and for σ-ideals I and J of R, IJ ⊆ P implies that I ⊆ P or J ⊆ P . A proper ideal Q of R is σ-semiprime ideal of Q if Q is a σ-ideal and for a σ-ideal I of R, I2 ⊆ Q implies that I ⊆ Q. The σ-prime radical is defined by the intersection of all σ-prime ideals of R and is denoted by Pσ(R). In this paper, the following results are obtained: (1) For a principal ideal domain R, Pσ(R) is the smallest σ-semiprime ideal of R; (2) For any ring R with an automorphism σ and for a skew Laurent polynomial ring R[x, x−1; σ], the prime radical of R[x, x−1; σ] is equal to Pσ(R)[x, x−1; σ].
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