Enochs, Edgar E.; Jenda, Overtoun M. G. Copure injective resolutions, flat resolvents and dimensions. (English) Zbl 0780.18006 Commentat. Math. Univ. Carol. 34, No. 2, 203-211 (1993). 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. Cited in 20 Documents 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, Künneth formula (category-theoretic aspects) Keywords:resolutions; copure injective preenvelopes over Noetherian rings; copure flat preenvelopes over commutative Artinian rings; \(n\)-Gorenstein rings PDFBibTeX XMLCite \textit{E. E. Enochs} and \textit{O. M. G. Jenda}, Commentat. Math. Univ. Carol. 34, No. 2, 203--211 (1993; Zbl 0780.18006) Full Text: EuDML