The existence of envelopes
Edgar E. Enochs, Overtoun M. G. Jenda, Jinzhong Xu (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Edgar E. Enochs, Overtoun M. G. Jenda, Jinzhong Xu (1993)
Rendiconti del Seminario Matematico della Università di Padova
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Edgar E. Enochs, Jenda M. G. Overtoun (1993)
Commentationes Mathematicae Universitatis Carolinae
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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 -Gorenstein rings. As a consequence, if the full subcategory of strongly copure injective (respectively flat) modules over a left and right noetherian ring has cokernels (respectively kernels), then is -Gorenstein.
Xiao Guang Yan, Xiao Sheng Zhu (2011)
Czechoslovak Mathematical Journal
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Let be a commutative ring and a semidualizing -module. We investigate the relations between -flat modules and -FP-injective modules and use these modules and their character modules to characterize some rings, including artinian, noetherian and coherent rings.
L. Fuchs (1969)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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