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Pure-injective hulls of modules over valuation rings
Francois Couchot
If R\hat{R}\otimes\_RMMM$. Moreove…
Injective modules and fp-injective modules over valuation rings
Francois Couchot
It is shown that each almost maximal valuation ring R such that every indecomposable injective module is countably generated, satisfies the following condition (C): each fp-injecti…
Modules with RD-composition series over a commutative ring
Francois Couchot
If R is a commutative ring, we prove that every finitely generated module has a pure-composition series with indecomposable factors and any two such series are isomorphic if and on…
The lambda-dimension of commutative arithmetic rings
Francois Couchot
It is shown that every commutative arithmetic ring has -dimension . An example of a commutative Kaplansky ring with -dimension 3 is given. If satis…
RD-flatness and RD-injectivity
Francois Couchot
It is proved that every commutative ring whose RD-injective modules are -RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of…
Finitely presented modules over semihereditary rings
Francois Couchot
One proves that each almost local-global semihereditary ring has the stacked basis property and is almost Bezout. If M is a finitely presented module, its torsion part tM is a dire…
Local rings of bounded module type are almost maximal valuation rings
Francois Couchot
It is shown that every commutative local ring of bounded module type is an almost maximal valuation ring.