2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66585Given a finite alphabet X and an ordering on the letters, the map σsends 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 <σ(I)> generated by σ(I) in the free monoid is finitely generated. Whether there exists an ordering such that <σ(I)> is finitely generated turns out to be NP-complete. The latter problem is closely related to the recognition problem for comparability graphs.27 pages, 2 postscript figures, uses gastex.styCommutative AlgebraCombinatoricsGroup Theory13P10;68R15;05C17;16Z05;68Q25text