Injective vector valued semigroups.
Invertibility criterion of composition of two multiary quasigroups
We study invertibility of operations that are composition of two operations of arbitrary arities. We find the criterion for quasigroups and specifications for -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.: Orthogonal hypercubes and -ary operations, Quasigroups Related Systems 13 (2005), no. 1, 73–86]. We establish...