A generalization of an inequality of Lech relating multiplicity and colength*
A generalization of an inequality of Lech relating multiplicity and colength*
复制标题
与多重性和 colength 有关的 Lech 不等式的推广*
DOI：
--
复制
发表时间：
2017
影响因子：
0.7
通讯作者：
Javid Validashti
中科院分区：
文献类型：
--
作者：
C. Huneke;I. Smirnov;Javid Validashti
本文研究了Lech关于等特征局部环中有限色长理想的重数与其色长之间关系的一个公式的特殊推广，并证明了其中一个推广涉及极大理想乘有限色长理想的重数。我们还提出了一个Lech型公式，涉及多重性和发电机的数量。我们在三维空间中证明了这个猜想，并建立了一个更弱的结果。
Abstract We study conjectured generalizations of a formula of Lech which relates the multiplicity of a finite colength ideal in an equicharacteristic local ring to its colength and prove one of these generalizations involving the multiplicity of the maximal ideal times the finite colength ideal. We also propose a Lech-type formula that relates multiplicity and the number of generators. We prove the conjecture in dimension three and establish a weaker result in full generality.