Hilbert–Kunz function

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

$f(q)=\operatorname {length} _{R}(R/m^{[q]})$

where $m^{[q]}$ is the ideal generated by the q-th power 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