强拟序剩余系统中的弱不可约滤波器

Pub Date : 2021-12-15 DOI:10.47443/cm.2021.0032

D. Romano

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引用次数: 1

摘要

本文引入并分析了强拟有序剩余系统中弱不可约滤波器的概念。证明了任何弱不可约滤波器都是素数(因此是不可约的)滤波器。还证明了如果强拟序剩余系统A中所有滤子的格F(A)是分配的，则A中的任何不可约滤子在A中是弱不可约的。

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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Weakly Irreducible Filter in Strong Quasi-Ordered Residuated Systems

In this article, the notion of weakly irreducible filters in strong quasi-ordered residuated systems is introduced and analyzed. It is shown that any weakly irreducible filter is a prime (and therefore, irreducible) filter. It is also proved that if the lattice F(A) of all filters in a strong quasi-ordered residuated system A is distributive, then any irreducible filter in A is weakly irreducible in A.

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