Hilbert–Kunz Multiplicity and an Inequality between Multiplicity and Colength☆
Hilbert–Kunz Multiplicity and an Inequality between Multiplicity and Colength☆
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Hilbert–Kunz 重数以及重数与 Colength 之间的不等式☆
DOI：
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发表时间：
2000
期刊：
影响因子：
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通讯作者：
KEN
中科院分区：
文献类型：
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作者：
Kei;KEN
本文研究了具有小Hilbert-Kunz重数的局部环。特别地，我们证明了Hilbert-Kunz重数为1的非混合局部环是正则的，并对Hilbert-Kunz重数小于等于2的二维Cohen-Macaulay局部环进行了分类，同时，我们还研究了参数理想的紧闭包的重数与弦长之间的不等式，这与通常的重数与弦长之间的不等式相反.
Abstract In this paper, we study local rings of small Hilbert–Kunz multiplicity. In particular, we prove that an unmixed local ring of Hilbert–Kunz multiplicity one is regular and classify two-dimensional Cohen–Macaulay local rings whose Hilbert–Kunz multiplicity is 2 or less. Also, we investigate the inequality between the multiplicity and the colength of the tight closure of parameter ideals inverse to the usual inequality between multiplicity and colength.