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Copure injective resolutions, flat resolvents and dimensions. (English) Zbl 0780.18006

Summary: 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.

MSC:

18G10 Resolutions; derived functors (category-theoretic aspects)
16D50 Injective modules, self-injective associative rings
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
18G05 Projectives and injectives (category-theoretic aspects)
18G15 Ext and Tor, generalizations, K√ľnneth formula (category-theoretic aspects)
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