Extension of Grün's lemma results to vertex algebras

Adapt the Grün's lemma results for semiassociative Mal'cev algebras to two-sorted vertex algebras.

Background

Two-sorted vertex algebras do not form a Mal'cev variety of two-sorted algebras, so the general theorem in the paper does not apply directly. Nevertheless, they are constructed from sorts of abelian groups and lattice-ordered rings. The paper therefore raises the unresolved question of whether its results, or suitable analogues of them, can be transferred to vertex algebras despite the absence of a Mal'cev-variety framework.