2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/125152It is proved that a commutative ring is clean if and only if it is Gelfand with a totally disconnected maximal spectrum. Commutative rings for which each indecomposable module has a local endomorphism ring are studied. These rings are clean and elementary divisor rings.Rings and Algebras13C05, 13A99text