2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/140688We compare, for smooth monomial projective curves, the Castel- nuovo-Mumford regularity and the reduction number; we present an example where these two numbers differ. However, we show they coin- cide for a certain class of monomial curves. Furthermore, for smooth monomial curves we prove an inequality which is stronger than the one from the Eisenbud-Goto conjecture.9 pagesCommutative Algebra13A30; 13D45text