2003/01/08 by Francois Couchot, François Couchot
Mathematics · #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #Rings, Modules, and Algebras #math.RA
paper · pdf · doi:10.1081/agb-120022218
published as Communications in Algebra 31 (2003) 3171-3194
openalex publication_date 2003/01/08 · arxiv created 2004/09/27 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
If R is a commutative ring,then we prove that every finitely generated R-module has a pure-composition series with indecomposable cyclic factors and any two such series are isomorphic if and only if R is a Bézout ring and a CF-ring. When R is a such ring,the length of a pure-composition series of a finitely generated R-module M is compared with its Goldie dimension and we prove that these numbers are equal if and only if M is a direct sum of cyclic modules. We also give an example of an artinian module over a noetherian domain,which has an RD-composition series with uniserial factors. Finally we prove that every pure-injective R-module is RD-injective if and only if R is an arithmetic ring.