Cotorsion pairs generated by modules of bounded projective dimension

Details Cotorsion pairs generated by modules of bounded projective dimension Cotorsion pairs generated by modules of bounded projective dimension

2007-07-13

arxiv.org/abs/0707.2026v2

Mathematics

Rings and Algebras

30 Pages

Scientific paper

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 $\aleph_0$-noetherian ring Q of small 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 Cohen Macaulay noetherian commutative rings.

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