Cohen-Macaulay Algebraic Monoids

Algebraic Shifting and Sequentially Cohen-Macaulay Simplicial Complexes

Björner and Wachs generalized the definition of shellability by dropping the assumption of purity; they also introduced the h-triangle, a doubly-indexed generalization of the h-vector which is combinatorially significant for nonpure shellable complexes. Stanley subsequently defined a nonpure simplicial complex to be sequentially Cohen-Macaulay if it satisfies algebraic conditions that generaliz...

Bi-Cohen-Macaulay graphs

In this paper we consider bi-Cohen-Macaulay graphs, and give a complete classification of such graphs in the case they are bipartite or chordal. General biCohen-Macaulay graphs are classified up to separation. The inseparable bi-CohenMacaulay graphs are determined. We establish a bijection between the set of all trees and the set of inseparable bi-Cohen-Macaulay graphs.

Cohen-macaulay Cell Complexes

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...

On Cohen-Macaulay rings

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.

Cohen-macaulay F -injective Homomorphisms