On a problem by Nathan Jacobson for Malcev algebras

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 ${\mathfrak{s}\mathfrak{l}}_2(\mathbb{F})$ such that $m,\mathfrak{s l}_{2}($\mathbb{F}$)\neq 0$forany$0\neq m\in$\mathcal{M}$.$ We drop the last condition and we describe the structure of the same class of Malcev algebras $\mathcal{M}$ that contains ${\mathfrak{s}\mathfrak{l}}_2(\mathbb{F})$.