2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/121453We determine the sublattice generated by the Miller-Morita-Mumford classes $κ_i$ in the torsion free quotient of the integral cohomology ring of the stable mapping class group. We further decide when the mod p reductions $κ_i$ vanish.24 pages, 1 figureAlgebraic TopologyAlgebraic Geometry57R20, 55P47text