  We study algebraic conditions when a pseudo MV-algebra is an interval in the
lexicographic product of an Abelian unital $\ell$-group and an $\ell$-group
that is not necessary Abelian. We introduce $(H,u)$-perfect pseudo MV-algebras
and strong $(H,u)$-perfect pseudo MV-algebras, the latter ones will have a
representation by a lexicographic product. Fixing a unital $\ell$-group
$(H,u)$, the category of strong $(H,u)$-perfect pseudo MV-algebras is
categorically equivalent to the category of $\ell$-groups.
