On function algebras in which every congruence is determined by a filter (Q807656)

It is proved that for certain universal algebras A there is a bijection between the congruences on \(A^ X\) and the filters on X. From this result a description of all left ideals of the near-ring of all functions of a group G to itself is obtained. Moreover, the well-known result concerning the simplicity of this near-ring for \(| G| >2\) follows almost immediately. Finally, function algebras are studied, where every invariant subalgebra is determined by its image.