Fitting Conditions for Symmetric Algebras of Modules of Finite Projective Dimension

Ionescu, Cristodor ; Restuccia, Gaetana ; Utano, Rosanna

Bollettino dell'Unione Matematica Italiana, Tome 10-A (2007), p. 681-696 / Harvested from Biblioteca Digitale Italiana di Matematica

Abstract

Let $E$ be a finitely generated $R$-module, having finite projective dimension. We study the acyclicity of the approximation complex $\mathcal{Z}(E)$ of $E$ in terms of certain Fitting conditions $F_k^{(i)}$ on the Fitting ideals of the $i$-th module of a projective resolution of $E$. We deduce some good properties of the symmetric algebra of $E$.

Résumé

Sia $E$ un $R$-modulo finitamente generato, di dimensione proiettiva finita. Studiamo l'aciclicità del complesso di approssimazione $\mathcal{Z}(E)$ di $E$ in termini di certe condizioni Fitting $F_k^{(i)}$ sugli ideali Fitting dell'$i$-esimo modulo di una risoluzione proiettiva di $E$. Ne deduciamo alcune buone proprietà dell'algebra simmetrica di $E$.

Détail

Publié le : 2007-10-01

MR 2351537 | Zbl 1177.13021

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