Wang's theorem for one-dimensional local rings

Jun Horiuchi; Hideto Sakurai

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Wang's theorem for one-dimensional local rings

机译：一维局部环的王定理

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In this article, we show that, Q :_A m~t is contained in m~t for all integers t ＞ 0, and for all parameter ideals Q is contained in m~(2t-1) in a one-dimensional Cohen-Macaulay local ring (A,m) provided that A is not a regular local ring. The assertion obtained by Wang can be extended to one-dimensional (hence, arbitrary dimensional) local rings after some mild modifications. We refer to these quotient ideals I = Q: _A m~t, t-th quasi-socle ideals of Q. Examples are explored.

机译：在本文中，我们证明，对于一维Cohen-，对于所有整数t＞ 0，Q：_A m〜t包含在m〜t中，对于所有参数理想，Q都包含在m〜（2t-1）中。如果A不是常规的本地环，Macaulay本地环（A，m）。经过一些轻微的修改，Wang获得的断言可以扩展到一维（因此为任意维）局部环。我们参考这些商理想I = Q：Q的第t个准晶理想。

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来源
《Journal of the Mathematical Society of Japan》 |2014年第2期|641-646|共6页
作者
Jun Horiuchi; Hideto Sakurai;
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作者单位

Department of Mathematics Nippon Institute of Technology Miyashiro Saitama 345-8501, Japan;

Department of Liberal Arts Toyama National College of Technology 1-2 Ebieneriya, Imizu-shi Toyama 933-0293, Japan;

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收录信息美国《科学引文索引》(SCI);
原文格式 PDF
正文语种 eng
中图分类
关键词
parameter ideal; quasi-socle ideal; Cohen-Macaulay local ring; Buchsbaum local ring;

机译：参数理想准太阳理想Cohen-Macaulay本地环;布斯鲍姆本地戒指;

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7. Local cohomology over homogeneous rings with one-dimensional local base ring [O] . Brodmann, M, Fumasoli, S, Tajarod, R 2003

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Wang's theorem for one-dimensional local rings

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