多项式环中素理想的形式纤维
Formal Fibers of Prime Ideals in Polynomial Rings
摘要：
设（R，m）是一个n维的诺特局部整环，它本质上是域上的n维生成的，R_n表示R的m-adic完备化. Matsumura证明了n-1是R^的素理想在R的一般形式纤维中的最大可能高度。本文证明了R^的每一个在R的一般形式纤维中极大的素理想都有高度n-1。本文还给出了混合多项式-幂级数环某些扩张的一般形式纤维的一个相关结果。
英文摘要：
Let (R,m) be a Noetherian local domain of dimension n that is essentially finitely generated over a field and let R^ denote the m-adic completion of R. Matsumura has shown that n-1 is the maximal height possible for prime ideals of R^ in the generic formal fiber of R. In this article we prove that every prime ideal of R^ that is maximal in the generic formal fiber of R has height n-1. We also present a related result concerning the generic formal fibers of certain extensions of mixed polynomial-power series rings.
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。
