2003/06/09 by Shirô Gotô, Shiro Goto, Goto, Shiro +2
Mathematics · Medicine · #13B22(Primary) #13H10(Secondary) #Algebraic structures and combinatorial models #Cholinesterase and Neurodegenerative Diseases #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #math.AC
paper · pdf · doi:10.48550/arxiv.math/0306148
26 pages, Rendiconti del Seminario Matematico dell'Universit di Padova (to appear)
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
Let A be a Noetherian local ring with the maximal ideal m and d=dimA. Let Q be a parameter ideal in A. Let I=Q:m. The problem of when the equality I2=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, while nothing is known when A is not a Cohen-Macaulay ring. The present purpose is to show that within a huge class of Buchsbaum local rings A the equality I2=QI holds true for all parameter ideals Q. The result will supply theorems of K. Yamagishi, S. Goto and K. Nishida with ample examples of ideals I, for which the Rees algebras R(I), the associated graded rings G(I), and the fiber cones F(I) are all Buchsbaum rings with certain specific graded local cohomology modules. Two examples are explored. One is to show that I2=QI may hold true for all parameter ideals Q in A, even though A is not a generalized Cohen-Macaulay ring, and the other one is to show that the equality I2=QI may fail to hold for some parameter ideal Q in A, even though A is a Buchsbaum local ring with multiplicity at least three.