Homological properties of balanced CohenMacaulay algebras
Author:
Izuru Mori
Journal:
Trans. Amer. Math. Soc. 355 (2003), 10251042
MSC (2000):
Primary 16W50, 16E05, 16E65, 16E10
Published electronically:
October 24, 2002
MathSciNet review:
1938744
Fulltext PDF Free Access
Abstract 
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Additional Information
Abstract: A balanced CohenMacaulay algebra is a connected algebra having a balanced dualizing complex in the sense of Yekutieli (1992) for some integer and some graded  bimodule . We study some homological properties of a balanced CohenMacaulay algebra. In particular, we will prove the following theorem: As a corollary, we will have the following characterizations of AS Gorenstein algebras and AS regular algebras:
 1.
M. Artin and J. J. Zhang, Noncommutative Projective Schemes, Adv. Math. 109 (1994), 228287. MR 96a:14004
 2.
M. Auslander and R. Buchweitz, The Homological Theory of Maximal CohenMacaulay Approximations, Mem. Soc. Math. de France 38 (1989), 537. MR 91h:13010
 3.
L. L. Avramov and H.B. Foxby, Homological Dimensions of Unbounded Complexes, J. of Pure and Appl. Algebra 71 (1991), 129155. MR 93g:18017
 4.
L. L. Avramov and H.B. Foxby, Ring Homomorphisms and Finite Gorenstein Dimensions, Proc. London Math. Soc. (3) 75 (1997), 241270. MR 98d:13014
 5.
P. Jörgensen, Local Cohomology for Noncommutative Graded Algebras, Comm. Algebra 25 (1997), 575591. MR 97j:16013
 6.
P. Jörgensen, Noncommutative Graded Homological Identities, J. London Math. Soc. (2) 57 (1998), 336350. MR 99h:16010
 7.
P. Jörgensen, Properties of ASCohenMacaulay Algebras, J. of Pure and Appl. Algebra 138 (1999), 239249. MR 2000c:16014
 8.
P. Jörgensen, Gorenstein Homomorphisms of Noncommutative Rings, J. Algebra 211 (1999), 240267. MR 2000c:16013
 9.
P. Jörgensen and J. J. Zhang, Gourmet's Guide to Gorensteinness, Adv. Math. 151 (2000), 313345. MR 2001d:16023
 10.
I. Mori, Intersection Multiplicity over Noncommutative Algebras, J. Algebra 252 (2002), 241257.
 11.
S. P. Smith, Noncommutative Algebraic Geometry, lecture notes, University of Washington, (1994).
 12.
M. Van den Bergh, Existence Theorems for Dualizing Complexes over Noncommutative Graded and Filtered Rings, J. Algebra 195 (1997), 662679. MR 99b:16010
 13.
A. Yekutieli, Dualizing Complexes over Noncommutative Graded Algebras, J. Algebra 153 (1992), 4184. MR 94a:16077
 1.
 M. Artin and J. J. Zhang, Noncommutative Projective Schemes, Adv. Math. 109 (1994), 228287. MR 96a:14004
 2.
 M. Auslander and R. Buchweitz, The Homological Theory of Maximal CohenMacaulay Approximations, Mem. Soc. Math. de France 38 (1989), 537. MR 91h:13010
 3.
 L. L. Avramov and H.B. Foxby, Homological Dimensions of Unbounded Complexes, J. of Pure and Appl. Algebra 71 (1991), 129155. MR 93g:18017
 4.
 L. L. Avramov and H.B. Foxby, Ring Homomorphisms and Finite Gorenstein Dimensions, Proc. London Math. Soc. (3) 75 (1997), 241270. MR 98d:13014
 5.
 P. Jörgensen, Local Cohomology for Noncommutative Graded Algebras, Comm. Algebra 25 (1997), 575591. MR 97j:16013
 6.
 P. Jörgensen, Noncommutative Graded Homological Identities, J. London Math. Soc. (2) 57 (1998), 336350. MR 99h:16010
 7.
 P. Jörgensen, Properties of ASCohenMacaulay Algebras, J. of Pure and Appl. Algebra 138 (1999), 239249. MR 2000c:16014
 8.
 P. Jörgensen, Gorenstein Homomorphisms of Noncommutative Rings, J. Algebra 211 (1999), 240267. MR 2000c:16013
 9.
 P. Jörgensen and J. J. Zhang, Gourmet's Guide to Gorensteinness, Adv. Math. 151 (2000), 313345. MR 2001d:16023
 10.
 I. Mori, Intersection Multiplicity over Noncommutative Algebras, J. Algebra 252 (2002), 241257.
 11.
 S. P. Smith, Noncommutative Algebraic Geometry, lecture notes, University of Washington, (1994).
 12.
 M. Van den Bergh, Existence Theorems for Dualizing Complexes over Noncommutative Graded and Filtered Rings, J. Algebra 195 (1997), 662679. MR 99b:16010
 13.
 A. Yekutieli, Dualizing Complexes over Noncommutative Graded Algebras, J. Algebra 153 (1992), 4184. MR 94a:16077
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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, 132441150
Email:
mori@math.purdue.edu, imori@syr.edu
DOI:
http://dx.doi.org/10.1090/S0002994702031665
PII:
S 00029947(02)031665
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
