The equality I²=QI in Buchsbaum rings with multiplicity two

2003/06/09 by Shirô Gotô, Shiro Goto, Goto, Shiro +2
Mathematics · #13B22(Primary) #13H10(Secondary) #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC

paper · pdf · doi:10.48550/arxiv.math/0306146

13 pages

arxiv created 2003/06/09 · openalex publication_date 2003/06/09 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 I²=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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