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Keywords:
preenvelopes; copure injective; copure flat; $n$-Gorenstein; resolutions
preenvelopes; copure injective; copure flat; $n$-Gorenstein; resolutions
Summary:
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.
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