  An algebra is said to be hopfian if it is not isomorphic to a proper quotient
of itself. We describe several classes of hopfian and of non-hopfian unital
lattice-ordered abelian groups and MV-algebras. Using Elliott classification
and $K_0$-theory, we apply our results to other related structures, notably the
Farey-Stern-Brocot AF C$^*$-algebra and all its primitive quotients, including
the Behnke-Leptin C$^*$-algebras $\mathcal A_{k,q}$.
