Weak Global Dimension of Coherent Rings |
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| Authors: | Lixin Mao |
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| Institution: | 1. Department of Mathematics , Nanjing University , Nanjing, China;2. Institute of Mathematics, Nanjing Institute of Technology , Nanjing, China |
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| Abstract: | 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 ? ? the class of all FP-injective left R-modules. It is shown that wD(R) ≤ n (n ≥ 1) if and only if every nth ? ?-syzygy of a left R-module is FP-injective; and wD(R) ≤ n (n ≥ 2) if and only if every (n ? 2)th ? ?-syzygy in a minimal ? ?-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. |
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| Keywords: | FP-injective dimension (Pre)cover Syzygy Weak global dimension |
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