English

A computation of tight closure in diagonal hypersurfaces

Commutative Algebra 2007-05-23 v1

Abstract

In the ring R=K[X,Y,Z]/(X^3+Y^3+Z^3), where K is a field of prime characteristic p other than 3, determining the tight closure of the ideal (X^2, Y^2, Z^2)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[X_1,...,X_n]/(X_1^n + ... + X_n^n).

Keywords

Cite

@article{arxiv.math/0209239,
  title  = {A computation of tight closure in diagonal hypersurfaces},
  author = {Anurag K. Singh},
  journal= {arXiv preprint arXiv:math/0209239},
  year   = {2007}
}
R2 v1 2026-07-22T16:47:45.253Z