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Ore Extensions Over (a,s)-Rings

Journal Name:

  • European Journal of Pure and Applied Mathematics

Publication Year:

  • 2015

Key Words:

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Abstract (2. Language): 
Let R be a Noetherian, integral domain which is also an algebra over Q (Q is the field of rational numbers). Let  be an automorphism of R and  a -derivation of R. A ring R is called a (,)-ring if a((a)+(a)) ∈ P(R) implies that a ∈ P(R) for a ∈ R, where P(R) is the prime radical of R. We prove that R is 2-primal if (P(R)) ⊆ P(R). We also study the property of minimal prime ideals of R and prove the following in this direction: Let R be a Noetherian, integral domain which is also an algebra over Q. Let  be an automorphism of R and  a -derivation of R such that R is a (,)-ring. If P ∈ Min.Spec(R) is such that (P) = P, then (P) ⊆ P. Further if (P(R)) ⊆ P(R), then P[x;,] is a completely prime ideal of R[x;,]. 2010 Mathematics Subject Classifications: 16-XX, 16W20, 16P40, 16S50
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REFERENCES

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