Utano, R.; Restuccia, G. Integrity of the symmetric algebra of modules of projective dimension two. (English) Zbl 0882.13025 Riv. Mat. Univ. Parma, V. Ser. 4, 193-204 (1995). 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. Reviewer: S.Balcerzyk (Toruń) Cited in 1 Review 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) Keywords:integral domain property; Cohen-Macaulay integral domain; projective dimension 2; symmetric algebra; depth; exterior powers PDFBibTeX XMLCite \textit{R. Utano} and \textit{G. Restuccia}, Riv. Mat. Univ. Parma, V. Ser. 4, 193--204 (1995; Zbl 0882.13025)