重数序列与整数依赖
Multiplicity sequence and integral dependence
摘要：
证明了等维泛悬链线Noether局部环中任意两个理想$I \subset J$具有相同的整闭包当且仅当它们具有相同的重数序列.我们还得到了一个积分依赖的特殊化原理，它给出了族中重数序列恒定的积分依赖的条件。
英文摘要：
We prove that two arbitrary ideals $I \subset J$ in an equidimensional and universally catenary Noetherian local ring have the same integral closure if and only if they have the same multiplicity sequence. We also obtain a Principle of Specialization of Integral Dependence, which gives a condition for integral dependence in terms of the constancy of the multiplicity sequence in families.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
