Homological properties of balanced Cohen-Macaulay algebras

Mori, Izuru

doi:10.1090/S0002-9947-02-03166-5

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
DOI: https://doi.org/10.1090/S0002-9947-02-03166-5
Published electronically: October 24, 2002
MathSciNet review: 1938744
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Abstract: A balanced Cohen-Macaulay algebra is a connected algebra having a balanced dualizing complex $\omega_A[d]$ in the sense of Yekutieli (1992) for some integer and some graded - 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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