In algebra, the Hilbert–Kunz function of a local ring (R, m) of prime characteristic p is the function f ( q ) = length R ( R / m [ q ] ) {\displaystyle 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 Ernst Kunz, who used it to characterize a regular ring as a Noetherian ring in which the Frobenius morphism is flat.
In algebra, the Hilbert–Kunz function of a local ring (R, m) of prime characteristic p is the function f ( q ) = length R ( R / m [ q ] ) {\displaystyle 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 Ernst Kunz, who used it to characterize a regular ring as a Noetherian ring in which the Frobenius morphism is flat.
Source: Wikipedia "Hilbert–Kunz function" · CC BY-SA 4.0
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