The equality I^2=QI in Buchsbaum rings with multiplicity two

doi:https://doi.org/10.48550/arxiv.math/0306146

Open AccessPreprint10.48550/arxiv.math/0306146

The equality I^2=QI in Buchsbaum rings with multiplicity two

Shirô Gotô,Hideto Sakurai-2003-06-09-ArXiv.org

TL;DRAbstract

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^2=QI holds true, if e(A)=2 and depthA>0. The assertion is no longer true, unless e(A)=2. Counterexamples are given.

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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^2=QI holds true, if e(A)=2 and depthA>0. The assertion is no longer true, unless e(A)=2. Counterexamples are given.

Keywords

Multiplicity (mathematics)Local ringMathematicsPure mathematicsPolitical scienceRing (chemistry)GeometryChemistry

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