Geodesic
Copure injective resolutions, flat resolvents and dimensions
Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 2, pp. 203-211.

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In this paper, we show the existence of copure injective preenvelopes over noetherian rings and copure flat preenvelopes over commutative artinian rings. We use this to characterize $n$-Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring $R$ has cokernels (respectively kernels), then $R$ is $2$-Gorenstein.
Classification : 13H10, 16D50, 16E30, 18G05, 18G10, 18G15
Keywords: preenvelopes; copure injective; copure flat; $n$-Gorenstein; resolutions 
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Enochs, Edgar E.; Overtoun, Jenda M. G. Copure injective resolutions, flat resolvents and dimensions. Commentationes Mathematicae Universitatis Carolinae, Tome 34 (1993) no. 2, pp. 203-211. http://geodesic.mathdoc.fr/item/CMUC_1993__34_2_a1/