2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78220We consider the lattice of subsemigroups of the general linear group over an Artinian ring containing the group of diagonal matrices and show that every such semigroup is actually a group.Plain TeX, 6 pages; final version accepted for publication in Semigroup ForumGroup Theory20M20; 20E07; 20E15; 20G15; 20G35text