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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. [1]
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.
References
Conca, Aldo (1996). "Hilbert-Kunz function of monomial ideals and binomial hypersurfaces" (PDF). http://www.dima.unige.it. Springer Verlag 90, 287 - 300. Retrieved 23 August 2014.
Bibliography
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.
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