Cotorsion pairs generated by modules of bounded projective dimension

We apply the theory of cotorsion pairs to study closure properties of classes of modules with finite projective dimension with respect to direct limit operations and to filtrations. We also prove that if the ring is an order in an א0-noetherian ring Q of little finitistic dimension 0, then the cotorsion pair generated by the modules of projective dimension at most one is of finite type if and only if Q has big finitistic dimension 0. This applies, for example, to semiprime Goldie rings and to Cohen Macaulay noetherian commutative rings. Our results allow us to give a positive answer to an open problem on the structure of divisible modules of projective dimension one over commutative domains posed in [23, Problem 6, p. 139]. We also give some insight on the structure of modules of finite weak dimension, giving a counterexample to [25, Open Problem 3, p. 187]. © 2009 Hebrew University Magnes Press.