A Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety

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dc.creatorJaiyeola, Temitope Gbolahan
dc.date2008-01-16
dc.date2008-06-05
dc.date.accessioned2026-07-07T09:42:31Z
dc.date.available2026-07-07T09:42:31Z
dc.descriptionThe isotopic invariance or universality of types and varieties of quasigroups and loops described by one or more equivalent identities has been of interest to researchers in loop theory in the recent past. A variety of quasigroups(loops) that are not universal have been found to be isotopic invariant relative to a special type of isotopism or the other. Presently, there are two outstanding open problems on universality of loops: semi automorphic inverse property loops(1999) and Osborn loops(2005). Smarandache isotopism(S-isotopism) was originally introduced by Vasantha Kandasamy in 2002. But in this work, the concept is re-restructured in order to make it more explorable. As a result of this, the theory of Smarandache isotopy inherits the open problems as highlighted above for isotopy. In this short note, the question 'Under what type of S-isotopism will a pair of S-quasigroups(S-loops) form any variety?' is answered by presenting a pair of specially S-isotopic S-quasigroups(loops) that both belong to the same variety of S-quasigroups(S-loops). This is important because pairs of specially S-isotopic S-quasigroups(e.g Smarandache cross inverse property quasigroups) that are of the same variety are useful for applications(e.g cryptography).
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0801.2513
dc.identifierhttp://arxiv.org/abs/0801.2513
dc.identifierInternational Journal of Mathematical Combinatorics, Vol 1(2008), 36-44
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/162210
dc.subjectGeneral Mathematics
dc.subject20NO5; 08A05
dc.titleA Pair of Smarandachely Isotopic Quasigroups and Loops of the Same Variety
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