Irreducible Polyadic Semigroups Admitting the Adjunction of a Neutral Element

Jean-Luc Marichal, Pierre Mathonet, Tamás Waldhauser

It was claimed in [4] that for any integer $n⩾2$, a neutral element can be adjoined to an $n$-ary semigroup if and only if the $n$-ary semigroup is reducible to a binary s…