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SM ISO690:2012 DUDEK, Wieslaw, MONZO, Robert. Double magma associated with Ward and double Ward quasigroups. In: Quasigroups and Related Systems, 2019, vol. 27, nr. 1(41), pp. 33-52. ISSN 1561-2848. |
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Quasigroups and Related Systems | ||||||
Volumul 27, Numărul 1(41) / 2019 / ISSN 1561-2848 | ||||||
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CZU: 512.548.7+512.816 | ||||||
MSC 2010: 20M15, 20N02. | ||||||
Pag. 33-52 | ||||||
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Rezumat | ||||||
We determine types of double magma associated with Ward quasigroups, double Ward quasigroups, their duals and the groups they generate. Ward quasigroup double magma and unipotent, right modular, left-unital double magma are proved to be improper. Necessary and sucient conditions are found on a pair of right modular, left unital magma (and right-left unital magma) for them to form a double magma. We give further insight into the intimate connection between the property of mediality and the interchange law by proving that a quasigroup is medial if and only if any pair of its parastrophic binary operations satisfy the interchange law. |
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Cuvinte-cheie Double magma, Ward quasigroup, doubleWard quasigroup, unipotent quasigroup, interchange law, parastrophe |
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Dublin Core Export
<?xml version='1.0' encoding='utf-8'?> <oai_dc:dc xmlns:dc='http://purl.org/dc/elements/1.1/' xmlns:oai_dc='http://www.openarchives.org/OAI/2.0/oai_dc/' xmlns:xsi='http://www.w3.org/2001/XMLSchema-instance' xsi:schemaLocation='http://www.openarchives.org/OAI/2.0/oai_dc/ http://www.openarchives.org/OAI/2.0/oai_dc.xsd'> <dc:creator>Dudek, W.A.</dc:creator> <dc:creator>Monzo, R.A.</dc:creator> <dc:date>2019-07-01</dc:date> <dc:description xml:lang='en'><p>We determine types of double magma associated with Ward quasigroups, double Ward quasigroups, their duals and the groups they generate. Ward quasigroup double magma and unipotent, right modular, left-unital double magma are proved to be improper. Necessary and sucient conditions are found on a pair of right modular, left unital magma (and right-left unital magma) for them to form a double magma. We give further insight into the intimate connection between the property of mediality and the interchange law by proving that a quasigroup is medial if and only if any pair of its parastrophic binary operations satisfy the interchange law.</p></dc:description> <dc:source>Quasigroups and Related Systems 41 (1) 33-52</dc:source> <dc:subject>Double magma</dc:subject> <dc:subject>Ward quasigroup</dc:subject> <dc:subject>doubleWard quasigroup</dc:subject> <dc:subject>unipotent quasigroup</dc:subject> <dc:subject>interchange law</dc:subject> <dc:subject>parastrophe</dc:subject> <dc:title>Double magma associated with Ward and double Ward quasigroups</dc:title> <dc:type>info:eu-repo/semantics/article</dc:type> </oai_dc:dc>