Hilbert–Kunz function: Difference between revisions

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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 regular rings as a ring in which a Frobenius morphism is flat module.

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

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 In algebra, the '''Hilbert–Kunz function''' of a local ring (''R'', ''m'') of characteristic ''p'' is the [[function (mathematics)|function]]
 :<math>f(q) = \operatorname{length}_R(R/m^{[q]})</math>
-where <math>m^{[q]}</math> is the ideal generated by the ''q''-th power of elements of the maximal ideal ''m''.
+where <math>m^{[q]}</math> 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 [[regular ring]]s as a ring in which a [[Frobenius morphism]] is [[flat module]].
 == References ==
 *Aldo Conca, [http://www.dima.unige.it/%7Econca/Articoli%20Conca%20PDF/PDF%20da%20rivista/%281996%20%29%20Conca%20-%20Hilbert-Kunz%20function%20of%20monomial%20ideals%20and%20binomial%20hypersurfaces.pdf 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
 {{algebra-stub}}