On a Class of N-ary Quasigroups
Branka Alimpić (1981)
Publications de l'Institut Mathématique
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Branka Alimpić (1981)
Publications de l'Institut Mathématique
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Jaiyéọlá, T.G., Adéníran, J.O. (2010)
Surveys in Mathematics and its Applications
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A. Nourou Issa (2000)
Commentationes Mathematicae Universitatis Carolinae
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Some properties of quasigroups with the left loop property are investigated. In loops we point out that the left loop property is closely related to the left Bol identity and the particular case of homogeneous loops is considered.
Natalia Didurik, Viktor Alekseevich Shcherbakov (2020)
Commentationes Mathematicae Universitatis Carolinae
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We proceed with Kunen's research about existence of units (left, right, two-sided) in quasigroups with classical Bol--Moufang type identities, listed in paper Extra loops II, by F. Fenyves (1969). We consider those Bol--Moufang identities where it has not been decided yet whether a quasigroup fulfilling this identity has to possess a left or right identity. We also provide a table of all Moufang--Bol identities, indicating at each whether it describes the variety of groups, and whether...
Tomáš Kepka, Michael K. Kinyon, Jon D. Phillips (2008)
Commentationes Mathematicae Universitatis Carolinae
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In Kepka T., Kinyon M.K., Phillips J.D., , J. Algebra (2007), 435–461, we showed that every F-quasigroup is linear over a special kind of Moufang loop called an NK-loop. Here we extend this relationship by showing an equivalence between the class of (pointed) F-quasigroups and the class corresponding to a certain notion of generalized module (with noncommutative, nonassociative addition) for an associative ring.