2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143619We study prime monomial algebras. Our main result is that a prime finitely presented monomial algebra is either primitive or it has GK dimension one and satisfies a polynomial identity. More generally, we show this result holds for the class of \emph{automaton algebras}; that is, monomial algebras that have a basis consisting of the set of words recognized by some finite state automaton. This proves a special case of a conjecture of the first author and Agata Smoktunowicz.3 figuresRings and Algebras16P90text