On some subtraction Menger algebras of multiplace functions (Q343481)

An \((n+1)\)-ary groupoid \((G, o)\), i.e., a nonempty set \(G\) with one \((n+1)\)-ary operation \(o:G^{n+1}\to G\) is called a Menger function of rank \(n\) if it satisfies the superassociativity law: \[ o(o(x,y_1,\dots, y_n),z_1,\dots, z_n)=o(x,o(y_1,z_1,\dots, z_n),\dots,o(y_n,z_1,\dots, z_n)). \] In this paper, the authors give an abstract characterization of algebras of some partial functions \(f:A^n\to A\) endowed with the operations of Menger superposition and set-theoretic difference of functions as subsets of \(A^{n+1}\). It is also proved that these classes are varieties.