Hilbert–Kunz function: Difference between revisions
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== References == |
== References == |
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*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] |
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==Bibliography== |
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*E. Kunz, "On noetherian rings of characteristic p," Am. J. Math, 98, (1976), 999–1013. 1 |
*E. Kunz, "On noetherian rings of characteristic p," Am. J. Math, 98, (1976), 999–1013. 1 |
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*{{cite arXiv |first1=Lance |last1=Edward Miller |first2=Irena |last2=Swanson |url=http://arxiv.org/abs/1206.1015 |title=Hilbert-Kunz functions of 2 x 2 determinantal rings |year=2012 |eprint=1206.1015}} |
*{{cite arXiv |first1=Lance |last1=Edward Miller |first2=Irena |last2=Swanson |url=http://arxiv.org/abs/1206.1015 |title=Hilbert-Kunz functions of 2 x 2 determinantal rings |year=2012 |eprint=1206.1015}} |
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Revision as of 22:12, 23 August 2014
In algebra, the Hilbert–Kunz function of a local ring (R, m) of prime characteristic p is the function
![{\displaystyle f(q)=\operatorname {length} _{R}(R/m^{[q]})}](https://wikimedia.org/enwiki/api/rest_v1/media/math/render/svg/0f3f8f6f04b331d9044200a42e11ab8351885954)
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 E. 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.
{{cite web}}: External link in|website=|publisher=at position 20 (help); line feed character in|title=at position 13 (help)
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.
{{cite arXiv}}: Unknown parameter|url=ignored (help)
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