Cotorsion pairs generated by modules of bounded projective dimension |
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Authors: | Silvana Bazzoni Dolors Herbera |
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Institution: | 1.Dipartimento di Matematica Pura e Applicata,Università di Padova,Padova,Italy;2.Departament de Matemàtiques,Universitat Autònoma de Barcelona,Bellaterra (Barcelona),Spain |
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Abstract: | 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. |
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Keywords: | |
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