We describe in homological terms the direct limit closure of a class of modules over a ring. We also determine the closure of the cotorsion pair generated by a set of finitely presented modules. As an application, we solve a problem of Fuchs and Salce on the structure of direct limits of modules of projective dimension at most one over commutative domains. Then we consider the case of the class of all finitely presented modules of finite projective dimension over a right coherent ring.
Direct limits of modules of finite projective dimension
ANGELERI, LIDIA;
2004-01-01
Abstract
We describe in homological terms the direct limit closure of a class of modules over a ring. We also determine the closure of the cotorsion pair generated by a set of finitely presented modules. As an application, we solve a problem of Fuchs and Salce on the structure of direct limits of modules of projective dimension at most one over commutative domains. Then we consider the case of the class of all finitely presented modules of finite projective dimension over a right coherent ring.
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