Weak global dimension of coherent rings

摘要

In this article, we study the weak global dimension of coherent rings in terms of the left FP-injective resolutions of modules. Let R be a left coherent ring and F I the class of all FP-injective left R-modules. It is shown that wD(R) <= n (n >= 1) if and only if every nth F I-syzygy of a left R-module is FP-injective; and wD(R) <= n (n >= 2) if and only if every (n - 2)th F I-syzygy in a minimal F I-resolution of a left R-module has an FP-injective cover with the unique mapping property. Some results for the weak global dimension of commutative coherent rings are also given.