The concept of a k-translatable groupoid is LYCOPENE 10MG explored in depth.Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k-translatablegroupoids are proved.Necessary and sufficient conditions are found for a left cancellative k-translatable groupoid to be a semigroup.
Any such semigroup is proved to be left unitary and a union disjoint copies of cyclic groups of the same order.Methods B12 W FOLIC of constructing k-translatable semigroups that are not left cancellative are given.