Translatability and translatable semigroups

Translatability and translatable semigroups

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The concept of a k-translatable groupoid is explored in depth.Some properties laguna 3hp dust collector 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 read more left unitary and a union disjoint copies of cyclic groups of the same order.Methods of constructing k-translatable semigroups that are not left cancellative are given.