On the structure of the canonical model of the Rees algebra and the associated graded ring of an ideal.

Let A be a noetherian local commutative ring and let M be a suitable complex of A-modules. It is proved that M is a dualizing complex for A if and only if the trivial extension A ⋉ M is a Gorenstein differential graded algebra. As a corollary, A has a dualizing complex if and only if it is a quotient of a Gorenstein local differential graded algebra.

On the Chern Number of a Filtration

Maria Evelina Rossi, Giuseppe Valla (2009)

Rendiconti del Seminario Matematico della Università di Padova

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Homological properties of some Weyl algebra extensions

Eva Kristina Ekström (1990)

Compositio Mathematica

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A corollary to the Evans-Griffith Syzygy theorem

Anne-Marie Simon (1995)

Rendiconti del Seminario Matematico della Università di Padova

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On the Gorenstein property of the diagonals of the Rees algebra.

Olga Lavila-Vidal, Santiago Zarzuela (1998)

Collectanea Mathematica

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On Cohen-Macaulay rings

Edgar E. Enochs, Jenda M. G. Overtoun (1994)

Commentationes Mathematicae Universitatis Carolinae

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In this paper, we use a characterization of $R$ -modules $N$ such that $f d_{R} N = p d_{R} N$ to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting $N$ to be the $d t h$ local cohomology functor of $R$ with respect to the maximal ideal where $d$ is the Krull dimension of $R$ .