  In this paper we solve a problem for a certain class of Malcev algebras,
which is an analogous of an old problem posed by Nathan Jacobson for
alternative algebras. Specifically we prove a coordinatization theorem for a
class of Malcev algebras containing the 3-dimensional simple Lie algebra
$\mathfrak{s l}_{2}(\mathbb{F})$ such that $m\,\mathfrak{s
l}_{2}(\mathbb{F})\neq 0$ for any $0\neq m\in\mathcal{M}.$ We drop the last
condition and we describe the structure of the same class of Malcev algebras
$\mathcal{M}$ that contains $\mathfrak{s l}_{2}(\mathbb{F})$.
