Indecomposable modules and Gelfand rings
arXiv:math/0510068 · doi:10.1080/00927870601041615
Abstract
It 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.