A computation of tight closure in diagonal hypersurfaces

2002/09/18 by Anurag K. Singh
Mathematics · #math.AC #msc:13A35

paper · pdf

published as Journal of Algebra {\bf 203} (1998) 579--589

arxiv created 2002/09/18 · arxiv updated 2009/11/30

Abstract

In the ring R=K[X,Y,Z]/(X³+Y³+Z³), where K is a field of prime characteristic p other than 3, determining the tight closure of the ideal (X², Y², Z²)R had existed as a classic example of the difficulty involved in tight closure computations. We settle this question, compute the Frobenius closure of this ideal, and generalize these results to the diagonal hypersurfaces K[X₁,...,X_n]/(X₁ⁿ + ... + X_nⁿ).

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