Copure injective resolutions, flat resolvents and dimensions

Edgar E. Enochs; Jenda M. G. Overtoun

Commentationes Mathematicae Universitatis Carolinae (1993)

  • Volume: 34, Issue: 2, page 203-211
  • ISSN: 0010-2628

Abstract

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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.

How to cite

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Enochs, Edgar E., and Overtoun, Jenda M. G.. "Copure injective resolutions, flat resolvents and dimensions." Commentationes Mathematicae Universitatis Carolinae 34.2 (1993): 203-211. <http://eudml.org/doc/247464>.

@article{Enochs1993,
abstract = {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.},
author = {Enochs, Edgar E., Overtoun, Jenda M. G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {preenvelopes; copure injective; copure flat; $n$-Gorenstein; resolutions; resolutions; copure injective preenvelopes over Noetherian rings; copure flat preenvelopes over commutative Artinian rings; -Gorenstein rings},
language = {eng},
number = {2},
pages = {203-211},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Copure injective resolutions, flat resolvents and dimensions},
url = {http://eudml.org/doc/247464},
volume = {34},
year = {1993},
}

TY - JOUR
AU - Enochs, Edgar E.
AU - Overtoun, Jenda M. G.
TI - Copure injective resolutions, flat resolvents and dimensions
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1993
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 34
IS - 2
SP - 203
EP - 211
AB - 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.
LA - eng
KW - preenvelopes; copure injective; copure flat; $n$-Gorenstein; resolutions; resolutions; copure injective preenvelopes over Noetherian rings; copure flat preenvelopes over commutative Artinian rings; -Gorenstein rings
UR - http://eudml.org/doc/247464
ER -

References

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