Tue, 24 Oct 2023, 1:25 pm MDT

A clonoid from an algebra A to an algebra B is a set of functions from finite powers of A into B that is closed under composition with term operations of A on the domain side and under composition with term operations of B on the codomain. We investigate clonoids from one module to another. When A and B are finite modules of coprime order (and the submodule lattice of A is distributive) we show that each clonoid from A to B is finitely generated and the lattice of clonoids from A to B is finite. We then extend these results to finite abelian Mal’cev algebras. We show how a 2-nilpotent Mal’cev algebra can be classified with the help of an associated clonoid between abelian Mal’cev algebras. This is joint work with Peter Mayr.