On Cohen-Macaulay rings

Edgar E. Enochs; Jenda M. G. Overtoun

Commentationes Mathematicae Universitatis Carolinae (1994)

  • Volume: 35, Issue: 2, page 223-230
  • ISSN: 0010-2628

Abstract

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In this paper, we use a characterization of R -modules N such that f d R N = p d R N to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting N to be the d t h local cohomology functor of R with respect to the maximal ideal where d is the Krull dimension of R .

How to cite

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Enochs, Edgar E., and Overtoun, Jenda M. G.. "On Cohen-Macaulay rings." Commentationes Mathematicae Universitatis Carolinae 35.2 (1994): 223-230. <http://eudml.org/doc/247640>.

@article{Enochs1994,
abstract = {In this paper, we use a characterization of $R$-modules $N$ such that $fd_RN = pd_RN$ to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting $N$ to be the $dth$ local cohomology functor of $R$ with respect to the maximal ideal where $d$ is the Krull dimension of $R$.},
author = {Enochs, Edgar E., Overtoun, Jenda M. G.},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {injective; precovers; preenvelopes; canonical module; Cohen-Macaulay; $n$-Gorenstein; resolvent; resolutions; flat dimension; projective dimension; Cohen-Macaulay ring},
language = {eng},
number = {2},
pages = {223-230},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On Cohen-Macaulay rings},
url = {http://eudml.org/doc/247640},
volume = {35},
year = {1994},
}

TY - JOUR
AU - Enochs, Edgar E.
AU - Overtoun, Jenda M. G.
TI - On Cohen-Macaulay rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 1994
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 35
IS - 2
SP - 223
EP - 230
AB - In this paper, we use a characterization of $R$-modules $N$ such that $fd_RN = pd_RN$ to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting $N$ to be the $dth$ local cohomology functor of $R$ with respect to the maximal ideal where $d$ is the Krull dimension of $R$.
LA - eng
KW - injective; precovers; preenvelopes; canonical module; Cohen-Macaulay; $n$-Gorenstein; resolvent; resolutions; flat dimension; projective dimension; Cohen-Macaulay ring
UR - http://eudml.org/doc/247640
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
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  8. Ishikawa T., On injective modules and flat modules, Math. Soc. Japan 17 (1965), 291-296. (1965) Zbl0199.07802MR0188272
  9. Jensen C., Les foncteurs dérivées de lim ← et leurs applications en théorie des modules, Lecture Notes in Mathematics 254, Springer, 1972. MR0407091
  10. Lenzing H., Endlich präsentierbare Moduln, Arch Math. 20 (1969), 262-266. (1969) Zbl0184.06501MR0244322
  11. Roberts P., Homological invariants of modules over commutative rings, Semin. Math. Super. 15, Presses Univ. Montreal, 1980. Zbl0467.13007MR0569936
  12. Strooker J., Homological questions in local algebra, London Math. Soc. Lecture Note Series 145, Cambridge Univ. Press, 1990. Zbl0786.13008MR1074178
  13. Yoshino Y., Cohen-Macaulay modules over Cohen-Macaulay rings, London Math. Soc. Lecture Note Series 146, Cambridge Univ. Press, 1990. Zbl0745.13003MR1079937

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