The Gorenstein property depends on characteristic (Q800431)

Using the characterization of the Gorenstein property of Stanley-Reisner rings in terms of the homology groups of the underlying simplicial complex and the dependence of the latter on the characteristic of the ground field k the author gives an example of a Stanley-Reisner ring k[\(\Delta]\) that is Gorenstein for \(char k\neq 2\) and not for \(char k=2.\) A theorem shows that k[\(\Delta]\) being Cohen-Macaulay over any field and Gorenstein over some field yields k[\(\Delta]\) being Gorenstein over any field. The given triangulation of \(P^ 3\) is false; it even fails to satisfy the generalized Dehn-Sommerville equations.