The factor of a subdirectly irreducible algebra through its monolith. (Q1771921)

Although every algebra whose signature contains at least one at least binary operation can be embedded into a subdirectly irreducible one, there exist algebras that are not homomorphic images of any subdirectly irreducible algebra. For algebras of the mentioned signature the authors prove that \(A\) is a homomorphic image of a subdirectly irreducible algebra if and only if the intersection of all of its ideals is nonempty. Let us note that their concept of ideal is different from that introduced in universal algebra and widely treated by A. Ursini and H. P. Gumm and others.