Invertibility criterion of composition of two multiary quasigroups
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Дата
2012
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Видавець
Czech Republic: COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE
Анотація
We study the Invertibility of operations that are a composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for T-quasigroups. For this purpose, we introduce notions of perpendicularity of operations and hypercubes. They differ from the previously introduced notions of orthogonality of operations and hypercubes [G. Belyavskaya, G. Mullen, Orthogonal hypercubes and n-ary operations, Quasigroups Related System 13 (2005), no. 1, 73-86]/ we establish some relations between these notions and give illustrative examples/
Опис
Article in the journal COMMENTATIONES MATHEMATICAE UNIVERSITATIS CAROLINAE (2012)
Ключові слова
quasigroup, composition of operations, orthogonal operations, perpendicular operations, hypercube, perpendicular hypercubes, orthogonality of hypercubes, slice, linear quasigroup, T-quasigroup