Hilbert–Kunz function

In algebra, the Hilbert–Kunz function of a local ring (R, m) of characteristic p is the function

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where m^[q] is the ideal generated by the q-th powers of elements of the maximal ideal m. The notion was introduced by E. Kunz, who used it to characterize a regular ring as a Noetherian ring in which the Frobenius morphism is flat.

References

• Aldo Conca, Hilbert-Kunz function of monomial ideals and binomial hypersurfaces
• E. Kunz, "On noetherian rings of characteristic p," Am. J. Math, 98, (1976), 999–1013. 1
• Edward Miller, Lance; Swanson, Irena (2012). "Hilbert-Kunz functions of 2 x 2 determinantal rings". arXiv:1206.1015. {{cite arXiv}}: Unknown parameter |url= ignored (help)