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A remark on the monomial conjecture and Cohen-Macaulay canonical modules
Author(s):
Le Thanh
Nhan
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2785-2794.
MSC (2000):
Primary 13D45, 13H10
Posted:
May 4, 2006
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Abstract:
In this paper, some sufficient conditions for rings and modules to satisfy the monomial conjecture are given. A characterization of Cohen-Macaulay canonical modules is presented.
References:
-
- [C]
- N. T. Cuong, On the dimension of non Cohen-Macaulay locus of local rings admitting dualizing complexes, Math. Proc. Camb. Soc., 109 (1991), 479-488. MR 1094747 (92b:13034)
- [CM]
- N. T. Cuong and N. D. Minh, Lengths of generalized fractions of modules having small polynomial type, Math. Proc. Camb. Phil. Soc., 128 (2000), 269-282. MR 1735305 (2001c:13036)
- [CHL]
- N. T. Cuong, N. T. Hoa and N. T. H. Loan, On certain length functions associated to a system of parameters in local rings, Vietnam J. Math., (3) 27 (1999), 259-272. MR 1811339 (2002d:13031)
- [CN]
- N. T. Cuong and L. T. Nhan, On pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay modules, J. Algebra, 267 (2003), 156-177. MR 1993472 (2004f:13012)
- [CMN]
- N. T. Cuong, M. Morales and L. T. Nhan, The finiteness of certain sets of attached prime ideals and the length of generalized fractions, J. Pure Appl. Algebra, (1-3) 189 (2004), 109-121. MR 2038567 (2004m:13046)
- [D]
- S. P. Dutta, A note on the monomial conjecture, Trans. AMS, (7) 350 (1998), 2871-2878. MR 1466948 (98i:13047)
- [Go]
- S. Goto, On the associated graded rings of parameter ideals in Buchsbaum rings, J. Algebra, 85 (1983), 490-534. MR 0725097 (85d:13032)
- [H1]
- M. Hochster, Contracted ideals from integral extensions of regular rings, Nagoya Math. J., 51 (1973), 25-43. MR 0349656 (50:2149)
- [H2]
- M. Hochster, Canonical elements in local cohomology modules and the direct summand conjecture, J. Algebra, 84 (1983), 503-553. MR 0723406 (85j:13021)
- [K]
- I. Kaplansky, Commutative Rings, Allyn and Bacon, Boston, 1970. MR 0254021 (40:7234)
- [Mac]
- I. G. Macdonald, Secondary representation of modules over a commutative ring, Symposia Mathematica, 11 (1973), 23-43. MR 0342506 (49:7252)
- [Sc]
- P. Schenzel, On birational Macaulayfications and Cohen-Macaulay canonical modules, J. Algebra, 275 (2004), 751-770. MR 2052635 (2005i:13017)
- [SH]
- R. Y. Sharp and M. A. Hamieh, Lengths of certain generalized fractions, J. Pure Appl. Algebra, 38 (1985), 323-336. MR 0814188 (87c:13031)
- [SZ1]
- R. Y. Sharp and H. Zakeri, Modules of generalized fractions, Mathematika, 29 (1982), 32-41. MR 0673503 (84a:13008)
- [SZ2]
- R. Y. Sharp and H. Zakeri, Generalized fractions and the monomial conjecture, J. Algebra, (2) 92 (1985), 380-388. MR 0778456 (86c:13013)
- [St]
- J. R. Strooker, Homological questions in local algebra, London Math. Lecture Notes Series, Vol. 145, Cambridge University Press, 1990. MR 1074178 (91m:13013)
- [SS]
- J. R. Strooker and J. Stückrad, Monomial conjecture and complete intersections, Manuscripta Math., 79 (1993), 153-159. MR 1216771 (94c:13026)
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Additional Information:
Le Thanh
Nhan
Affiliation:
Department of Mathematics, Thai Nguyen Pedagogical University, Thai Nguyen, Vietnam
Email:
trtrnhan@yahoo.com
DOI:
10.1090/S0002-9939-06-08573-X
PII:
S 0002-9939(06)08573-X
Keywords:
Monomial conjecture,
strict f-sequences,
Cohen-Macaulay canonical modules
Received by editor(s):
January 11, 2005
Posted:
May 4, 2006
Additional Notes:
The author is a junior associate member of ICTP, Trieste, Italy
Communicated by:
Bernd Ulrich
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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