局部n环的表征及其在抽象调和分析中的应用

Pub Date : 2023-06-01 DOI:10.1216/jca.2023.15.287

B. Wilkens

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摘要

摘要。一个具有单位的交换环，如果它的每一个理想都是由一个诺瑟扩展环缩并而成，就称为N环。本文的主要结果是局部N环的子直接不可约商的刻画。将所得结果用于表征阿贝尔群G上复值函数空间的G不变子空间上的谱合成。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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A CHARACTERISATION OF LOCAL N-RINGS AND AN APPLICATION TO ABSTRACT HARMONIC ANALYSIS

A BSTRACT . A commutative ring with unity is called an N -ring if each of its ideals is contracted from an Noetherian extension ring. The chief result of the paper is a characterisation of local N -rings by their subdirectly irreducible quotients. The results are applied to characterise spectral synthesis on G -invariant subspaces of the space of complex valued functions on an Abelian group G .

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