Abstract
We introduce weakly FP-injective and weakly flat functors, and we show that a right R-module K is FP-injective if and only if (−,K) is a flat weakly FP-injective functor in \({(({{\rm mod}-R})^{\rm op},{\rm Ab})}\), whereas a left R-module N is flat if and only if \({-\otimes N}\) is an FP-injective weakly flat functor in \({({{\rm mod}-R},{\rm Ab})}\). We give closure properties, we characterise classes of rings, and we study approximations by these classes of functors.
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This work was supported by the grant GSCE-2015-30253 of Babeş-Bolyai University of Cluj-Napoca. The author would like to thank the referee for the valuable suggestions, which improved the presentation and led to some new results in the last section of the paper.
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Crivei, S. Flat Weakly FP-Injective and FP-Injective Weakly Flat Functors. Results Math 71, 1031–1045 (2017). https://doi.org/10.1007/s00025-016-0598-8
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DOI: https://doi.org/10.1007/s00025-016-0598-8