Indecomposable modules and Gelfand rings

Francois Couchot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

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.

Mots clés: Gelfand ring; clean ring; indecomposable module; totally disconnected space

Domaines: Anneaux et algèbres [math.RA]

Francois Couchot. Indecomposable modules and Gelfand rings. Communications in Algebra, 2007, 35, pp.231--241. ⟨10.1080/00927870601041615⟩. ⟨hal-00009474v2⟩