Some necessary and sufficient conditions for parastrophic invariance of the associative law in quasigroups

• Autorzy: Jaiyeola T. G.
• Języki publikacji: EN

Abstrakty

EN

Every quasigroup (S, ⋅) belongs to a set of 6 quasi-groups, called parastrophes denoted by (S, π_i), i ∈ {1, 2, 3, 4, 5, 6}. It is shown that isotopy-isomorphy is a necessary and sufficient condition for any two distinct quasigroups (S, π_i) and (S, π_j), i, j ∈ {1, 2, 3, 4, 5, 6} to be parastrophic invariant relative to the associative law. In addition, a necessary and sufficient condition for any two distinct quasigroups (S, π_i) and (S, π_j), i, j ∈ {1, 2, 3, 4, 5, 6}. to be parastrophic invariant under the associative law is either if the π_i-parastrophe of H is equivalent to the π_i-parastrophe of the holomorph of the π_iparastrophe of S or if the π_i-parastrophe of H is equivalent to the π_k-parastrophe of the π_i-parastrophe of the holomorph of the π_i-parastrophe of S, for a particular k ∈ {1, 2, 3, 4, 5, 6}.

Słowa kluczowe

EN

parastrophes; associativity; quasigroups; isotopic; holomorphy

• Wydawca: Wydawnictwo Politechniki Poznańskiej
• Czasopismo: Fasciculi Mathematici
• Rocznik: 2008
• Tom: Nr 40
• Strony: 25--35
• Opis fizyczny: Bibliogr. 28 poz.

Twórcy

autor

Jaiyeola T. G.

• Department of Methematics, Obafemi Awolwo University, Ile Ife, Nigeria,

Bibliografia

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