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Integrity of the symmetric algebra of modules of projective dimension two. (English) Zbl 0882.13025

Let \(R\) be a Cohen-Macaulay integral domain containing a field and let \(E\) be a torsion free \(R\)-module of projective dimension 2 which admits a free resolution \(0 \to R^2 \to R^m \to R^n \to E \to 0\). The main result of the paper states that the symmetric algebra \(S(E)\) is an integral domain under a series of conditions on depths of some exterior powers of modules resulting from the resolution. The conditions are discussed in detail.

MSC:

13G05 Integral domains
13C15 Dimension theory, depth, related commutative rings (catenary, etc.)
13C05 Structure, classification theorems for modules and ideals in commutative rings
13D25 Complexes (MSC2000)
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