When is the category of flat modules abelian?

J. García; J. Martínez Hernández

Fundamenta Mathematicae (1995)

  • Volume: 147, Issue: 1, page 83-91
  • ISSN: 0016-2736

Abstract

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Let Fl(R) denote the category of flat right modules over an associative ring R. We find necessary and sufficient conditions for Fl(R) to be a Grothendieck category, in terms of properties of the ring R.

How to cite

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García, J., and Martínez Hernández, J.. "When is the category of flat modules abelian?." Fundamenta Mathematicae 147.1 (1995): 83-91. <http://eudml.org/doc/212076>.

@article{García1995,
abstract = {Let Fl(R) denote the category of flat right modules over an associative ring R. We find necessary and sufficient conditions for Fl(R) to be a Grothendieck category, in terms of properties of the ring R.},
author = {García, J., Martínez Hernández, J.},
journal = {Fundamenta Mathematicae},
keywords = {Abelian categories; coherent rings; Grothendieck categories; flat modules; Lambek torsion theory; minimal injective resolutions; flat-dominant dimension; weak global dimension; FTF-rings},
language = {eng},
number = {1},
pages = {83-91},
title = {When is the category of flat modules abelian?},
url = {http://eudml.org/doc/212076},
volume = {147},
year = {1995},
}

TY - JOUR
AU - García, J.
AU - Martínez Hernández, J.
TI - When is the category of flat modules abelian?
JO - Fundamenta Mathematicae
PY - 1995
VL - 147
IS - 1
SP - 83
EP - 91
AB - Let Fl(R) denote the category of flat right modules over an associative ring R. We find necessary and sufficient conditions for Fl(R) to be a Grothendieck category, in terms of properties of the ring R.
LA - eng
KW - Abelian categories; coherent rings; Grothendieck categories; flat modules; Lambek torsion theory; minimal injective resolutions; flat-dominant dimension; weak global dimension; FTF-rings
UR - http://eudml.org/doc/212076
ER -

References

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  13. [13] A. Rosenberg and D. Zelinsky, Finiteness of the injective hull, Math. Z. 70 (1959), 372-380. Zbl0084.26505
  14. [14] D. Simson, Functor categories in which every flat object is projective, Bull. Acad. Polon. Sci. 22 (1974), 375-380. Zbl0328.18005
  15. [15] D. Simson, On pure global dimension of locally finitely presented Grothendieck categories, Fund. Math. 96 (1977), 91-116. Zbl0361.18010
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