  A lexicographic pseudo MV-algebra is an algebra that is isomorphic to an
interval in the lexicographic product of a linear unital group with an
arbitrary $\ell$-group. We present conditions when a pseudo MV-algebra is
lexicographic. We show that a key condition is the existence of a lexicographic
ideal, or equivalently, a case when the algebra can be split into comparable
slices indexed by elements of the interval $[0,u]$ of some unital linearly
ordered group $(H,u)$. Finally, we show that fixing $(H,u)$, the category of
$(H,u)$-lexicographic pseudo MV-algebras is categorically equivalent to the
category of $\ell$-groups.
