We introduce a new family of simple graphs, so called, growing graphs. investigate ways to modify given graph G combinatorially obtain graph. One may infinitely many graphs from single show that obtained any is Cohen–Macaulay and every chordal also prove under certain conditions, if only its clique complex grafted give several equivalent conditions in this case. Our work inspired by generalizes...

We show that a finite regular cell complex with the intersection property is a Cohen-Macaulay space iff the top enriched cohomology module is the only nonvanishing one. We prove a comprehensive generalization of Balinski’s theorem on convex polytopes. Also we show that for any Cohen-Macaulay cell complex as above, although there is now generalization of the Stanley-Reisner ring of simplicial co...

A balanced Cohen-Macaulay algebra is a connected algebra A having a balanced dualizing complex ωA[d] in the sense of Yekutieli (1992) for some integer d and some graded A-A bimodule ωA. We study some homological properties of a balanced Cohen-Macaulay algebra. In particular, we will prove the following theorem: Theorem 0.1. Let A be a Noetherian balanced Cohen-Macaulay algebra, and M a nonzero ...

In [11], Haiman proved the remarkable result that the isospectral Hilbert scheme of points in the plane is normal, Cohen-Macaulay and Gorenstein. He also showed that this implies the n! conjecture and the positivity conjecture for the Kostka-Macdonald coefficients. In addition, he conjectured that the isospectral Hilbert scheme over the principal component of Hilb(Cd) is Cohen-Macaulay for any ...

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...