On functions commuting with semigroups of transformations of algebras (Q5932614)

The author introduces the notions of elementary conditionally termal and \(\exists\)-positive conditionally termal functions over an algebra \(A\) and proves that, whenever \(A\) is finite, every function \(f\) is elementary conditionally termal if and only if \(f\) commutes with all automorphisms of \(A\) and all subalgebras of \(A\) are closed under \(f\). A similar result is obtained for \(\exists\)-positive conditionally termal functions. Related questions are studied.