Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Homological properties of balanced Cohen-Macaulay algebras


Author: Izuru Mori
Journal: Trans. Amer. Math. Soc. 355 (2003), 1025-1042
MSC (2000): Primary 16W50, 16E05, 16E65, 16E10
Published electronically: October 24, 2002
MathSciNet review: 1938744
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A balanced Cohen-Macaulay algebra is a connected algebra $A$ having a balanced dualizing complex $\omega_A[d]$ in the sense of Yekutieli (1992) for some integer $d$ and some graded $A$-$A$ bimodule $\omega_A$. We study some homological properties of a balanced Cohen-Macaulay algebra. In particular, we will prove the following theorem:
 \begin{thm0} Let $A$\space be a Noetherian balanced Cohen-Macaulay algebra, and ... ...s^{r_0}_{j=1} \omega_A(-l_{0j})\to M\to 0. \end{align*}\end{enumerate}\end{thm0}

As a corollary, we will have the following characterizations of AS Gorenstein algebras and AS regular algebras:
 \begin{cor0} Let $A$\space be a Noetherian balanced Cohen-Macaulay algebra. \beg... ...ximal Cohen-Macaulay graded left $A$ -module is free. \end{enumerate}\end{cor0}


References [Enhancements On Off] (What's this?)

  • 1. M. Artin and J. J. Zhang, Noncommutative Projective Schemes, Adv. Math. 109 (1994), 228-287. MR 96a:14004
  • 2. M. Auslander and R. Buchweitz, The Homological Theory of Maximal Cohen-Macaulay Approximations, Mem. Soc. Math. de France 38 (1989), 5-37. MR 91h:13010
  • 3. L. L. Avramov and H.-B. Foxby, Homological Dimensions of Unbounded Complexes, J. of Pure and Appl. Algebra 71 (1991), 129-155. MR 93g:18017
  • 4. L. L. Avramov and H.-B. Foxby, Ring Homomorphisms and Finite Gorenstein Dimensions, Proc. London Math. Soc. (3) 75 (1997), 241-270. MR 98d:13014
  • 5. P. Jörgensen, Local Cohomology for Non-commutative Graded Algebras, Comm. Algebra 25 (1997), 575-591. MR 97j:16013
  • 6. P. Jörgensen, Non-commutative Graded Homological Identities, J. London Math. Soc. (2) 57 (1998), 336-350. MR 99h:16010
  • 7. P. Jörgensen, Properties of AS-Cohen-Macaulay Algebras, J. of Pure and Appl. Algebra 138 (1999), 239-249. MR 2000c:16014
  • 8. P. Jörgensen, Gorenstein Homomorphisms of Noncommutative Rings, J. Algebra 211 (1999), 240-267. MR 2000c:16013
  • 9. P. Jörgensen and J. J. Zhang, Gourmet's Guide to Gorensteinness, Adv. Math. 151 (2000), 313-345. MR 2001d:16023
  • 10. I. Mori, Intersection Multiplicity over Noncommutative Algebras, J. Algebra 252 (2002), 241-257.
  • 11. S. P. Smith, Non-commutative Algebraic Geometry, lecture notes, University of Washington, (1994).
  • 12. M. Van den Bergh, Existence Theorems for Dualizing Complexes over Non-commutative Graded and Filtered Rings, J. Algebra 195 (1997), 662-679. MR 99b:16010
  • 13. A. Yekutieli, Dualizing Complexes over Noncommutative Graded Algebras, J. Algebra 153 (1992), 41-84. MR 94a:16077

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 16W50, 16E05, 16E65, 16E10

Retrieve articles in all journals with MSC (2000): 16W50, 16E05, 16E65, 16E10


Additional Information

Izuru Mori
Affiliation: Department of Mathematics, Purdue University, West Lafayette, Indiana 47907
Address at time of publication: Department of Mathematics, Syracuse University, Syracuse, New York, 13244-1150
Email: mori@math.purdue.edu, imori@syr.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03166-5
PII: S 0002-9947(02)03166-5
Received by editor(s): October 10, 2001
Received by editor(s) in revised form: February 5, 2002
Published electronically: October 24, 2002
Article copyright: © Copyright 2002 American Mathematical Society