  Hahn's embedding theorem asserts that linearly ordered abelian groups embed
in some lexicographic product of real groups. Hahn's theorem is generalized to
a class of residuated semigroups in this paper, namely, to odd involutive
commutative residuated chains which possess only finitely many idempotent
elements. To this end, the partial sublex product construction is introduced to
construct new odd involutive commutative residuated lattices from a pair of odd
involutive commutative residuated lattices, and a representation theorem for
odd involutive commutative residuated chains which possess only finitely many
idempotent elements, by means of linearly ordered abelian groups and the
partial sublex product construction is presented.
