Let (R;m) be a local ring of Krull dimensiond andI ⊆R be an ideal with analytic spreadd. We show that thej-multiplicity ofI is determined by the Rees valuations ofI centered on m. We also discuss a multiplicity that is the limsup of a sequence of lengths that grow at anO(n ^d) rate.

中文翻译：

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多重性和里斯估值

让（[R M）是克鲁尔维数的本地环d和我⊆ - [R是一个与解析传播理想d。我们证明了I的j多重性是由以m为中心的I的Rees估值确定的。我们还将讨论多重性，即以O（n ^d）速率增长的长度序列的limsup 。