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Fitting conditions for symmetric algebras of modules of finite projective dimension. (English) Zbl 1177.13021

Summary: 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 \(E\).

MSC:

13Cxx Theory of modules and ideals in commutative rings
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