Interassociativity and three-element doppelsemigroups

Volodymyr Gavrylkiv, Diana Rendziak


In the paper  we characterize all interassociates of  some non-inverse semigroups and describe up to isomorphism all three-element (strong) doppelsemigroups and their automorphism groups. We prove that there exist 75 pairwise non-isomorphic three-element doppelsemigroups among which 41 doppelsemigroups are commutative. Non-commutative doppelsemigroups are divided into 17 pairs of dual doppelsemigroups. Also up to isomorphism there are 65 strong doppelsemigroups of order 3, and all non-strong doppelsemigroups are not commutative.


semigroup, interassociativity, doppelsemigroup, strong doppelsemigroup

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