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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  4. Enochs E., Jenda O., Balanced functors applied to modules, J. Algebra 92 (1985), 303-310. (1985) Zbl0554.18006MR0778450
  5. Enochs E., Jenda O., Resolvents and dimensions of modules and rings, Arch. Math. 56 (1991), 528-532. (1991) Zbl0694.16012MR1106493
  6. Enochs E., Jenda O., Copure injective modules, Quaest. Mathematicae 14 (1991), 401-409. (1991) Zbl0747.16003MR1143044
  7. Gabriel P., Objects injectifs dans les catégories abéliennes, Sém. Dubreil, 1958/59, 17/01-17/32, Paris, 1960. Zbl0214.03301
  8. Iwanaga Y., On rings with finite self-injective dimension II, Tsukuba J. Math. 4 (1980), 107-113. (1980) Zbl0459.16011MR0597688
  9. Jenda O., The dual of the grade of a module, Arch. Math. 51 (1988), 297-302. (1988) Zbl0632.16018MR0964954
  10. Jensen C., Les foncteurs derives de ø v e r s e t lim → ⟵ et leurs applications en theorie des modules, Lecture Notes in Mathematics 254, Springer, 1972. MR0407091
  11. Lenzing H., Endlich präsentierbare modulen, Arch. Math. 20 (1969), 262-266. (1969) MR0244322

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