Hilbert–Kunz function

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

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

where q is a power of p and 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)