  Given a finite alphabet X and an ordering on the letters, the map \sigma
sends each monomial on X to the word that is the ordered product of the letter
powers in the monomial. Motivated by a question on Groebner bases, we
characterize ideals I in the free commutative monoid (in terms of a generating
set) such that the ideal <\sigma(I)> generated by \sigma(I) in the free monoid
is finitely generated. Whether there exists an ordering such that <\sigma(I)>
is finitely generated turns out to be NP-complete. The latter problem is
closely related to the recognition problem for comparability graphs.
