The Equality I = Qi in Buchsbaum Rings with Multiplicity Two
نویسندگان
چکیده
Let A be a Buchsbaum local ring with the maximal ideal m and let e(A) denote the multiplicity of A. Let Q be a parameter ideal in A and put I = Q : m. Then the equality I = QI holds true, if e(A) = 2 and depth A > 0. The assertion is no longer true, unless e(A) = 2. Counterexamples are given.
منابع مشابه
The Equality I = Qi in Buchsbaum Rings
Let A be a Noetherian local ring with the maximal ideal m and d = dim A. Let Q be a parameter ideal in A. Let I = Q : m. The problem of when the equality I = QI holds true is explored. When A is a Cohen-Macaulay ring, this problem was completely solved by A. Corso, C. Huneke, C. Polini, and W. Vasconcelos [CHV, CP, CPV], while nothing is known when A is not a Cohen-Macaulay ring. The present pu...
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