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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
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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: https://doi.org/10.1090/S0002-9947-02-03166-5
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