Invertibility criterion of composition of two multiary quasigroups

Commentationes mathematicae Universitatis Carolinae

Fedir M. Sokhatsky¹ 

关键词: quasigroup;    composition of operations;    orthogonal operations;    perpendicular operations;    hypercube;    perpendicular hypercubes;    orthogonality of hypercubes;    slice;    linear quasigroup;    $T$-quasigroup;   

DOI  :  

学科分类：物理化学和理论化学

来源: Univerzita Karlova v Praze * Matematicko-Fyzikalni Fakulta / Charles University in Prague, Faculty of Mathematics and Physics

【 摘 要 】

We study invertibility of operations that are 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 [Belyavskaya G., Mullen G.L., {\it Orthogonal hypercubes and $n$-ary operations\/}, Quasigroups Related Systems {\bf 13} (2005), no.~1, 73--86]. We establish some relationships between these notions and give illustrative examples.

【 授权许可】

CC BY