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Homological properties of balanced Cohen-Macaulay algebras

Author(s): Izuru Mori
Journal: Trans. Amer. Math. Soc. 355 (2003), 1025-1042.
MSC (2000): Primary 16W50, 16E05, 16E65, 16E10
Posted: October 24, 2002
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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}

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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, 13244-1150
Email: mori@math.purdue.edu, imori@syr.edu

DOI: 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
Posted: October 24, 2002
Copyright of article: Copyright 2002, American Mathematical Society

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