## A remark on the monomial conjecture and Cohen-Macaulay canonical modules

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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

- Nguyễn Tụ’ Cu’ò’ng,
*On the dimension of the non-Cohen-Macaulay locus of local rings admitting dualizing complexes*, Math. Proc. Cambridge Philos. Soc.**109**(1991), no. 3, 479–488. MR**1094747**, DOI 10.1017/S0305004100069929 - Nguyen Tu Cuong and Nguyen Duc Minh,
*Lengths of generalized fractions of modules having small polynomial type*, Math. Proc. Cambridge Philos. Soc.**128**(2000), no. 2, 269–282. MR**1735305**, DOI 10.1017/S0305004199003941 - Nguyen Tu Cuong, Nguyen Thai Hoa, and Nguyen Thi Hong Loan,
*On certain length functions associated to a system of parameters in local rings*, Vietnam J. Math.**27**(1999), no. 3, 259–272. MR**1811339** - Nguyen Tu Cuong and Le Thanh Nhan,
*Pseudo Cohen-Macaulay and pseudo generalized Cohen-Macaulay modules*, J. Algebra**267**(2003), no. 1, 156–177. MR**1993472**, DOI 10.1016/S0021-8693(03)00225-4 - Nguyen Tu Cuong, Marcel Morales, and Le Thanh Nhan,
*The finiteness of certain sets of attached prime ideals and the length of generalized fractions*, J. Pure Appl. Algebra**189**(2004), no. 1-3, 109–121. MR**2038567**, DOI 10.1016/j.jpaa.2003.11.006 - S. P. Dutta,
*A note on the monomial conjecture*, Trans. Amer. Math. Soc.**350**(1998), no. 7, 2871–2878. MR**1466948**, DOI 10.1090/S0002-9947-98-02158-8 - Shiro Goto,
*On the associated graded rings of parameter ideals in Buchsbaum rings*, J. Algebra**85**(1983), no. 2, 490–534. MR**725097**, DOI 10.1016/0021-8693(83)90109-6 - M. Hochster,
*Contracted ideals from integral extensions of regular rings*, Nagoya Math. J.**51**(1973), 25–43. MR**349656**, DOI 10.1017/S0027763000015701 - Melvin Hochster,
*Canonical elements in local cohomology modules and the direct summand conjecture*, J. Algebra**84**(1983), no. 2, 503–553. MR**723406**, DOI 10.1016/0021-8693(83)90092-3 - Irving Kaplansky,
*Commutative rings*, Allyn and Bacon, Inc., Boston, Mass., 1970. MR**0254021** - I. G. Macdonald,
*Secondary representation of modules over a commutative ring*, Symposia Mathematica, Vol. XI (Convegno di Algebra Commutativa, INDAM, Rome, 1971) Academic Press, London, 1973, pp. 23–43. MR**0342506** - Peter Schenzel,
*On birational Macaulayfications and Cohen-Macaulay canonical modules*, J. Algebra**275**(2004), no. 2, 751–770. MR**2052635**, DOI 10.1016/j.jalgebra.2003.12.016 - R. Y. Sharp and M. A. Hamieh,
*Lengths of certain generalized fractions*, J. Pure Appl. Algebra**38**(1985), no. 2-3, 323–336. MR**814188**, DOI 10.1016/0022-4049(85)90020-9 - R. Y. Sharp and H. Zakeri,
*Modules of generalized fractions*, Mathematika**29**(1982), no. 1, 32–41. MR**673503**, DOI 10.1112/S0025579300012134 - R. Y. Sharp and H. Zakeri,
*Generalized fractions and the monomial conjecture*, J. Algebra**92**(1985), no. 2, 380–388. MR**778456**, DOI 10.1016/0021-8693(85)90128-0 - Jan R. Strooker,
*Homological questions in local algebra*, London Mathematical Society Lecture Note Series, vol. 145, Cambridge University Press, Cambridge, 1990. MR**1074178**, DOI 10.1017/CBO9780511629242 - Jan R. Strooker and Jürgen Stückrad,
*Monomial conjecture and complete intersections*, Manuscripta Math.**79**(1993), no. 2, 153–159. MR**1216771**, DOI 10.1007/BF02568334

## Additional Information

**Le Thanh Nhan**- Affiliation: Department of Mathematics, Thai Nguyen Pedagogical University, Thai Nguyen, Vietnam
- Email: trtrnhan@yahoo.com
- Received by editor(s): January 11, 2005
- Published electronically: May 4, 2006
- Additional Notes: The author is a junior associate member of ICTP, Trieste, Italy
- Communicated by: Bernd Ulrich
- © Copyright 2006
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**134**(2006), 2785-2794 - MSC (2000): Primary 13D45, 13H10
- DOI: https://doi.org/10.1090/S0002-9939-06-08573-X
- MathSciNet review: 2231599