An abstract characterization of De Morgan \({(2,5)}\)-semigroup of \(5\)-ary functions (Q2439441)

A De Morgan \((2,5)\)-semigroup is an algebra that can be seen as 5 monoids on the same domain and one unary operation (quasi-complementation) that connects the operations of these monoids in the manner of De Morgan laws in Boolean algebras. It is not clear why the authors study such algebras with exactly 5 semigroup operations. They translate notions of left zero element, ideal and congruence and provide necessary and sufficient conditions for a De Morgan \((2,5)\)-semigroup to be isomorphic with a De Morgan \((2,5)\)-semigroup of \(5\)-ary functions over a fixed set. The proof is omitted.