Regular sequences and minimal bases.
Regular sequences and minimal bases.
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规则序列和最小碱基。
DOI：
10.2140/pjm.1971.36.323
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发表时间：
1971
期刊：
影响因子：
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通讯作者：
E. Davis
中科院分区：
文献类型：
--
作者：
E. Davis
这篇笔记记录了努力简单地理解 Lichtenbaum 和 Schlessinger 的某个定理的结果：设 I D / 为诺特局部环的理想。如果/和///是由正则序列生成的，那么J也是如此。这个定理与众所周知的密切相关：如果R和R/P是正则局部环，那么P是由正则参数系统的一部分生成的。我们研究了“IIJ 由正则序列生成”的含义，并发现了一个将这两个结果作为推论的基本定理。
This note records the results of an effort to understand in simple terms a certain theorem of Lichtenbaum and Schlessinger : Let I D / be ideals of noetherian local ring. If / and /// are generated by regular sequences, then so is J. This theorem is closely related to the well known: If R and R/P are regular local rings, then P is generated by part of a regular system of parameters. We investigate the implications of " IIJ is generated by a regular sequence " and discover an elementary theorem having both of these results as corollaries.