In the winter of 1999 I gave a series of lectures at Queen’s university about some recent results concerning the Cohen-Macaulay property of invariants of Hopf algebras. Tony Geramita asked me to write up my notes for the Queen’s Papers, and I happily took up his suggestion. Although this article focuses on the proof of one main theorem (Theorem 2.11 on page 12), it has some of the character of ...

This paper determines when the Krull-Schmidt property holds for all finitely generated modules and for maximal Cohen-Macaulay modules over one-dimensional local rings with finite Cohen-Macaulay type. We classify all maximal CohenMacaulay modules over these rings, beginning with the complete rings where the Krull-Schmidt property is known to hold. We are then able to determine when the Krull-Sch...

In this paper, we use a characterization of R-modules N such that fdRN = pdRN to characterize Cohen-Macaulay rings in terms of various dimensions. This is done by setting N to be the dth local cohomology functor of R with respect to the maximal ideal where d is the Krull dimension of R.

Let [Formula: see text] be a simple undirected graph. The family of all matchings forms simplicial complex called the matching text]. Here, we give classification graphs with Gorenstein complex. Also study when is Cohen–Macaulay and, in certain classes graphs, fully characterize those which have In particular, graph girth at least five or complete Cohen–Macaulay.