  General theory determines the notion of separable MV-algebra (equivalently,
of separable unital lattice-ordered Abelian group). We establish the following
structure theorem: An MV-algebra is separable if, and only if, it is a finite
product of algebras of rational numbers, i.e., of subalgebras of the MV-algebra
$[0,1]\cap\mathbb{Q}$. Beyond its intrinsic algebraic interest, this research
is motivated by the long-term programme of developing the algebraic geometry of
the opposite of the categroy of MV-algebras, in analogy with the classical case
of commutative $K$-algebras over a field $K$.
