Characterization of clones of boolean operations by identities

Characterization of clones of boolean operations by identities

In [4] the authors characterized all clones of Boolean operations (Boolean clones) by functional terms. In this paper we consider a Galois connection between operations and equations and characterize all Boolean clones by using of identities. For each Boolean clone we obtain a set of equations with...

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Bibliographic Details
Date:2018
Main Authors: Butkote, Runglawan, Denecke, Klaus
Format: Article
Language:English
Published: Lugansk National Taras Shevchenko University 2018
Subjects:
Clone of Boolean operations
identity
Galois connection
03B05
03C05
08B05
Online Access:https://admjournal.luguniv.edu.ua/index.php/adm/article/view/844
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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-844
record_format ojs
spelling oai:ojs.admjournal.luguniv.edu.ua:article-8442018-03-21T11:59:09Z Characterization of clones of boolean operations by identities Butkote, Runglawan Denecke, Klaus Clone of Boolean operations, identity, Galois connection 03B05, 03C05, 08B05 In [4] the authors characterized all clones of Boolean operations (Boolean clones) by functional terms. In this paper we consider a Galois connection between operations and equations and characterize all Boolean clones by using of identities. For each Boolean clone we obtain a set of equations with the property that an operation \(f\) belongs to this clone if and only if it satisfies these equations. 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/844 Algebra and Discrete Mathematics; Vol 6, No 2 (2007) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/844/374 Copyright (c) 2018 Algebra and Discrete Mathematics
institution Algebra and Discrete Mathematics
baseUrl_str
datestamp_date 2018-03-21T11:59:09Z
collection OJS
language English
topic Clone of Boolean operations
identity
Galois connection
03B05
03C05
08B05
spellingShingle Clone of Boolean operations
identity
Galois connection
03B05
03C05
08B05
Butkote, Runglawan
Denecke, Klaus
Characterization of clones of boolean operations by identities
topic_facet Clone of Boolean operations
identity
Galois connection
03B05
03C05
08B05
format Article
author Butkote, Runglawan
Denecke, Klaus
author_facet Butkote, Runglawan
Denecke, Klaus
author_sort Butkote, Runglawan
title Characterization of clones of boolean operations by identities
title_short Characterization of clones of boolean operations by identities
title_full Characterization of clones of boolean operations by identities
title_fullStr Characterization of clones of boolean operations by identities
title_full_unstemmed Characterization of clones of boolean operations by identities
title_sort characterization of clones of boolean operations by identities
description In [4] the authors characterized all clones of Boolean operations (Boolean clones) by functional terms. In this paper we consider a Galois connection between operations and equations and characterize all Boolean clones by using of identities. For each Boolean clone we obtain a set of equations with the property that an operation \(f\) belongs to this clone if and only if it satisfies these equations.
publisher Lugansk National Taras Shevchenko University
publishDate 2018
url https://admjournal.luguniv.edu.ua/index.php/adm/article/view/844
work_keys_str_mv AT butkoterunglawan characterizationofclonesofbooleanoperationsbyidentities
AT deneckeklaus characterizationofclonesofbooleanoperationsbyidentities
first_indexed 2025-07-17T10:31:40Z
last_indexed 2025-07-17T10:31:40Z
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