Lattice embeddings in free Banach lattices over lattices

In this article we deal with the free Banach lattice generated by a and its behavior respect to subspaces. general, any embedding $i\colon \mathbb{L} \longrightarrow \mathbb{M}$ between two lattices $\mathbb{L} \subseteq induces homomorphism $\hat \imath\colon FBL \langle \rangle \mathbb{M}\rangle$ corresponding lattices. We show that mapping \imath$ might not be an isometric neither isomorphic embedding. order provide sufficient conditions for define notion of locally complemented prove that, if $\mathbb L$ is in M$, then yields from $FBL\langle\mathbb L\rangle$ into M\rangle$. wide number examples sublattices and, as application, obtain every AM-space or, equivalently, sublattice $C(K)$-space. Furthermore, only it injective, which turn equivalent fact $x^*\colon [-1,1]$ extends x^*\colon \mathbb{M} [-1,1]$. Using characterization example