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Indecomposable modules and Gelfand rings

Research paper by Francois Couchot

Indexed on: 07 Mar '07Published on: 07 Mar '07Published in: Mathematics - Rings and Algebras



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.