There isn’t much duality in radical theory

There isn’t much duality in radical theory

The definitions of radical and semi-simple classes are in a natural sense dual to each other. However, statements dual in the same sense to theorems of radical theory tend to be false. Some insights may nevertheless be gained from consideration of duality, and we illustrate this with a link between...

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Bibliographic Details
Date:2018
Main Author: Gardner, B. J.
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
radical class
semi-simple class
duality
16N80
16S90
18E40
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/858
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Journal Title:Algebra and Discrete Mathematics

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Algebra and Discrete Mathematics
id oai:ojs.admjournal.luguniv.edu.ua:article-858
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-8582018-03-21T12:28:31Z There isn’t much duality in radical theory Gardner, B. J. radical class, semi-simple class, duality 16N80, 16S90, 18E40 The definitions of radical and semi-simple classes are in a natural sense dual to each other. However, statements dual in the same sense to theorems of radical theory tend to be false. Some insights may nevertheless be gained from consideration of duality, and we illustrate this with a link between additive radicals and semi-simple radical classes. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/858 Algebra and Discrete Mathematics; Vol 6, No 3 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/858/388 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T12:28:31Z
collection OJS
language English
topic radical class
semi-simple class
duality
16N80
16S90
18E40
spellingShingle radical class
semi-simple class
duality
16N80
16S90
18E40
Gardner, B. J.
There isn’t much duality in radical theory
topic_facet radical class
semi-simple class
duality
16N80
16S90
18E40
format Article
author Gardner, B. J.
author_facet Gardner, B. J.
author_sort Gardner, B. J.
title There isn’t much duality in radical theory
title_short There isn’t much duality in radical theory
title_full There isn’t much duality in radical theory
title_fullStr There isn’t much duality in radical theory
title_full_unstemmed There isn’t much duality in radical theory
title_sort there isn’t much duality in radical theory
description The definitions of radical and semi-simple classes are in a natural sense dual to each other. However, statements dual in the same sense to theorems of radical theory tend to be false. Some insights may nevertheless be gained from consideration of duality, and we illustrate this with a link between additive radicals and semi-simple radical classes.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/858
work_keys_str_mv AT gardnerbj thereisntmuchdualityinradicaltheory
first_indexed 2025-07-17T10:31:41Z
last_indexed 2025-07-17T10:31:41Z
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