Residually Finite Algebra

An algebra for which any two distinct elements can be separated by a homomorphism to some finite algebra; equivalently the intersection of all finite-index congruences is the trivial congruence.

An algebra is residually finite if for every pair of distinct elements there exists a homomorphism from the algebra to some finite algebra that separates them (their images are distinct); equivalently the algebra embeds into a direct product of finite algebras.