The Complexity of Module Radicals

IF 0.6 3区数学 Q2 LOGIC

Notre Dame Journal of Formal Logic Pub Date : 2021-05-01 DOI:10.1215/00294527-2021-0017

Chris J. Conidis

引用次数: 3

Abstract

We construct a computable module M over a computable commutative ring R such that the radical of M, rad(M), defined as the intersection of all proper maximal submodules, is Π1-complete. This shows that in general such radicals are as (logically) complicated as possible and, unlike many other kinds of ring-theoretic radicals, admit no arithmetical definition.

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模基的复杂性

我们在一个可计算交换环R上构造一个可计算模M，使得M的根rad(M)，定义为所有固有极大子模的交，是Π1-complete。这表明，在一般情况下，这样的根是(逻辑上)尽可能复杂的，不像许多其他种类的环论根，承认没有算术定义。

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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来源期刊

Notre Dame Journal of Formal Logic MATHEMATICS-LOGIC

CiteScore

1.00

自引率

14.30%

发文量

审稿时长

>12 weeks

期刊介绍： The Notre Dame Journal of Formal Logic, founded in 1960, aims to publish high quality and original research papers in philosophical logic, mathematical logic, and related areas, including papers of compelling historical interest. The Journal is also willing to selectively publish expository articles on important current topics of interest as well as book reviews.