| Title:
|
On Cohen-Macaulay rings (English) |
| Author:
|
Enochs, Edgar E. |
| Author:
|
Overtoun, Jenda M. G. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
223-230 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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 $R$. (English) |
| Keyword:
|
injective |
| Keyword:
|
precovers |
| Keyword:
|
preenvelopes |
| Keyword:
|
canonical module |
| Keyword:
|
Cohen-Macaulay |
| Keyword:
|
\newline $n$-Gorenstein |
| Keyword:
|
resolvent |
| Keyword:
|
resolutions |
| MSC:
|
13C14 |
| MSC:
|
13D02 |
| MSC:
|
13D05 |
| MSC:
|
13D45 |
| MSC:
|
13H10 |
| MSC:
|
18G10 |
| MSC:
|
18G20 |
| idZBL:
|
Zbl 0816.13008 |
| idMR:
|
MR1286568 |
| . |
| Date available:
|
2009-01-08T18:10:27Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118660 |
| . |
| Reference:
|
[1] Auslander M., Buchweitz R.: The homological theory of maximal Cohen-Macaulay approximations.Soc. Math. de France, Memoire 38 (1989), 5-37. Zbl 0697.13005, MR 1044344 |
| Reference:
|
[2] Bass H.: On the ubiquity of Gorenstein rings.Math. Z. 82 (1963), 8-28. Zbl 0112.26604, MR 0153708 |
| Reference:
|
[3] Enochs E., Jenda O.: Copure injective resolutions, flat resolvents and dimensions.Comment. Math. Univ. Carolinae 34 (1993), 202-211. Zbl 0780.18006, MR 1241728 |
| Reference:
|
[4] Enochs E., Jenda O.: Balanced functors applied to modules.J. Algebra 92 (1985), 303-310. Zbl 0554.18006, MR 0778450 |
| Reference:
|
[5] Foxby H.-B.: Isomorphisms between complexes with applications to the homological theory of modules.Math. Scand. 40 (1977), 5-19. Zbl 0356.13004, MR 0447269 |
| Reference:
|
[6] Grothendieck A.: Local Cohomology.Lecture Notes in Mathematics 41, Springer, 1967. Zbl 1079.14001, MR 0224620 |
| Reference:
|
[7] Herzog J., Kunz E.: Der Kanonische Modul eines Cohen-Macaulay-Rings.Lecture Notes in Mathematics 238, Springer, 1971. Zbl 0231.13009, MR 0412177 |
| Reference:
|
[8] Ishikawa T.: On injective modules and flat modules.Math. Soc. Japan 17 (1965), 291-296. Zbl 0199.07802, MR 0188272 |
| Reference:
|
[9] Jensen C.: Les foncteurs dérivées de $\lim _{\leftarrow}$ et leurs applications en théorie des modules.Lecture Notes in Mathematics 254, Springer, 1972. MR 0407091 |
| Reference:
|
[10] Lenzing H.: Endlich präsentierbare Moduln.Arch Math. 20 (1969), 262-266. Zbl 0184.06501, MR 0244322 |
| Reference:
|
[11] Roberts P.: Homological invariants of modules over commutative rings.Semin. Math. Super. 15, Presses Univ. Montreal, 1980. Zbl 0467.13007, MR 0569936 |
| Reference:
|
[12] Strooker J.: Homological questions in local algebra.London Math. Soc. Lecture Note Series 145, Cambridge Univ. Press, 1990. Zbl 0786.13008, MR 1074178 |
| Reference:
|
[13] Yoshino Y.: Cohen-Macaulay modules over Cohen-Macaulay rings.London Math. Soc. Lecture Note Series 146, Cambridge Univ. Press, 1990. Zbl 0745.13003, MR 1079937 |
| . |
