Effective codescent morphisms of n-quasigroups and n-loops

D. Zangurashvili

Effective codescent morphisms of n-quasigroups and of n-loops are characterized. To this end, it is proved that, for any n ≥ 1, every codescent morphism of n-quasigroups (resp. n-loops) is effective. This statement generalizes our earlier result on quasigroups (resp. loops). Moreover, it is shown that the variety of n-quasigroups (resp. n-loops) satisfies the strong amalgamation property, and the elements of the amalgamated free products of n-quasigroups (resp. n-loops) have unique normal forms. The latter two statements generalize the corresponding old results on quasigroups (resp. loops) by T. Evans. 

Advanced Studies: Euro-Tbilisi Mathematical Journal, Vol. 17(3) (2024), pp. 53-62