Representing endomorphisms and principal congruences (Q1272247)

The authors prove that for every algebra \({\mathfrak A}\) there is an algebra \({\mathfrak A}^*\) with (up to isomorphism) the same endomorphism, subalgebra and congruence structures as \({\mathfrak A},\) for which every finitely generated subalgebra in \({\mathfrak A}^*\) is singly generated and every compact congruence on \({\mathfrak A}^*\) is principal.