Essential normality — a unified approach in terms of local decompositions
Essential normality — a unified approach in terms of local decompositions
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DOI：
10.1112/plms.12272
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发表时间：
2018-12
影响因子：
1.8
通讯作者：
Yi Wang
中科院分区：
文献类型：
--
作者：
Yi Wang
本文定义了La2（Bn）的子模的渐近稳定除法性质。我们证明了在一个温和的条件下，一个具有渐近稳定除法性质的子模对所有p>n都是p‐本质正态的。提出了一种新的证明子模具有渐近稳定除法性质的方法。这就统一证明了大多数已知的关于子模基本正态性的结果以及新的结果。特别地，我们证明了一个理想定义了La2（Bn）的p -本质正规子模∀p>n，如果它的相关原素理想是其零轨迹满足球面附近标准正则性条件的原素理想的幂。
In this paper, we define the asymptotic stable division property for submodules of La2(Bn) . We show that under a mild condition, a submodule with the asymptotic stable division property is p ‐essentially normal for all p>n . A new technique is developed to show that certain submodules have the asymptotic stable division property. This leads to a unified proof of most known results on essential normality of submodules as well as new results. In particular, we show that an ideal defines a p ‐essentially normal submodule of La2(Bn) , ∀p>n , if its associated primary ideals are powers of prime ideals whose zero loci satisfy standard regularity conditions near the sphere.