On the Koszul algebra of a local ring (Q1320926)

Let \(R\) be a noetherian local ring, \(H_ \bullet (R)\) the Koszul algebra of \(R\) and \(\lambda:\bigwedge H_ 1 (R) \to H_ \bullet (R)\) the canonical map of the exterior algebra \(\bigwedge H_ 1 (R)\) to \(H_ \bullet (R)\) extending the identity on \(H_ 1(R)\). It is proved that \(R\) is a complete intersection if and only if \(\lambda\) is injective.