Free summands of syzygies of modules over local rings (Q964539)

The author gives the following criterion for a commutative, noetherian, local ring to be Cohen-Macaulay: Theorem 2.4. A local ring \((A, \mathfrak m, k)\) is Cohen--Macaulay if and only if for some \(i > 0\), \(\mathrm{Syz}_i (A/x)\) has a free summand for some system of parameters \(x\) that form part of a minimal set of generators for \(\mathfrak m\).