The reduction number of stretched ideals
The reduction number of stretched ideals
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DOI：
10.2969/jmsj/86498649
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发表时间：
2021-09
影响因子：
0.7
通讯作者：
K. Ozeki
中科院分区：
文献类型：
--
作者：
K. Ozeki
理想的伴随分次环的同调性质是交换代数和代数几何中的一个重要问题。本文在Cohen-Macaulay局部环(A，m)的约化数达到几乎极小值的情况下，讨论了扩张m-素理想的伴随分次环的几乎Cohen-Macaulay性。作为应用，我们给出了具有小约化数的扩张m-素数理想的伴随分次环的完整刻划。
The homological property of the associated graded ring of an ideal is an important problem in commutative algebra and algebraic geometry. In this paper we explore the almost Cohen-Macaulayness of the associated graded ring of stretched m-primary ideals in the case where the reduction number attains almost minimal value in a Cohen-Macaulay local ring (A,m). As an application, we present complete descriptions of the associated graded ring of stretched m-primary ideals with small reduction number.