Cohen-macaulay Cell Complexes

Cohen-Macaulay-ness in codimension for simplicial complexes and expansion functor

In this paper we show that expansion of a Buchsbaum simplicial complex is $CM_t$, for an optimal integer $tgeq 1$. Also, by imposing extra assumptions on a $CM_t$ simplicial complex, we provethat it can be obtained from a Buchsbaum complex.

Gorenstein Injective Dimensions and Cohen-Macaulayness

Let (R,m) be a commutative noetherian local ring. In this paper we investigate the existence of a finitely generated R-module of finite Gorenstein dimension when R is Cohen-Macaulay. We study the Gorenstein injective dimension of local cohomology of complexes and next we show that if R is a non-Artinian Cohen-Macaulay ring, which does not have the minimal multiplicity, then R has a finite gener...

Sequentially Cohen-Macaulay Graphs of Form θ_{n1, ...nk}

A characterization of shellable and sequentially Cohen-Macaulay

We consider a class of hypergraphs called hypercycles and we show that a hypercycle $C_n^{d,alpha}$ is shellable or sequentially the Cohen--Macaulay if and only if $nin{3,5}$. Also, we characterize Cohen--Macaulay hypercycles. These results are hypergraph versions of results proved for cycles in graphs.

RESULTS ON ALMOST COHEN-MACAULAY MODULES

Let $(R,underline{m})$ be a commutative Noetherian local ring and $M$ be a non-zero finitely generated $R$-module. We show that if $R$ is almost Cohen-Macaulay and $M$ is perfect with finite projective dimension, then $M$ is an almost Cohen-Macaulay module. Also, we give some necessary and sufficient condition on $M$ to be an almost Cohen-Macaulay module, by using $Ext$ functors.