  One of the main goals of this paper is to present the relation of limit key
polynomials and limit MacLane-Vaqui\'e key polynomials. This is a continuation
of the work started in a paper by Decaup, Mahboub and Spivakovsky, where it is
proved the equivalent result for key polynomials (which are not limit).
Moreover, we present a result (Theorem 1.1) that generalizes various results in
the literature.
