985 citations · 12.2k across the 103 of their papers we have counts for
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Commutative rings whose finitely generated ideals are quasi-flat
Francois Couchot
A definition of quasi-flat left module is proposed and it is shown that any left module which is either quasi-projective or flat is quasi-flat. A characterization of local commutat…
Finitely generated powers of prime ideals
Francois Couchot
Let R be a commutative ring. If P is a maximal ideal of R whose a power is finitely generated then we prove that P is finitely generated if R is either locally coherent or arithmet…
Gaussian trivial ring extensions and fqp-rings
Francois Couchot
Let A be a commutative ring and E a non-zero A-module. Necessary and sufficient conditions are given for the trivial ring extension R of A by E to be either arithmetical or Gaussia…
Commutative rings whose cotorsion modules are pure-injective
Francois Couchot
Let R be a ring (not necessarily commutative). A left R-module is said to be cotorsion if Ext 1 R (G, M) = 0 for any flat R-module G. It is well known that each pure-injective left…
Rings whose indecomposable modules are pure-projective or pure-injective
François Couchot
Let be the class of rings for which every indecomposable right module is pure-projective or pure-injective. When is a Noetherian local commutative ring of maximal…
Comparison of some purities, flatnesses and injectivities
Walid Al-Kawarit, Francois Couchot
In this paper, we compare -purities for different pairs of positive integers . When is a commutative ring, these purities are not equivalent if doesn't satisf…