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May 2021 The Complexity of Module Radicals
Chris J. Conidis
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Notre Dame J. Formal Logic 62(2): 353-368 (May 2021). DOI: 10.1215/00294527-2021-0017

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 Π11-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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Chris J. Conidis. "The Complexity of Module Radicals." Notre Dame J. Formal Logic 62 (2) 353 - 368, May 2021. https://doi.org/10.1215/00294527-2021-0017

Information

Received: 12 August 2020; Accepted: 29 December 2020; Published: May 2021
First available in Project Euclid: 9 June 2021

Digital Object Identifier: 10.1215/00294527-2021-0017

Subjects:
Primary: 03D80
Secondary: 03F65

Rights: Copyright © 2021 University of Notre Dame

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Vol.62 • No. 2 • May 2021
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