Let (R,m) be a local Cohen-Macaulay ring whose m-adic completion R̂ has an isolated singularity. We verify the following conjecture of F.-O. Schreyer: R has finite Cohen-Macaulay type if and only if R̂ has finite Cohen-Macaulay type. We show also that the hypersurface k[[x0, . . . , xd]]/(f) has finite Cohen-Macaulay type if and only if k [[x0, . . . , xd]]/(f) has finite Cohen-Macaulay type, whe...

in this paper, we introduce a subclass of chordal graphs which contains $d$-trees and show that their complement are vertex decomposable and so is shellable and sequentially cohen-macaulay.

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x 1 ,. .. , x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and im...

In this paper, we characterize the shellable complete $t$-partite graphs. We also show for these types of graphs the concepts vertex decomposable, shellable and sequentially Cohen-Macaulay are equivalent. Furthermore, we give a combinatorial condition for the Cohen-Macaulay complete $t$-partite graphs.

In this paper we use "ring changed'' Gorenstein homologicaldimensions to define Cohen-Macaulay injective, projective and flatdimensions. For doing this we use the amalgamated duplication of thebase ring with semi-dualizing ideals. Among other results, we prove that finiteness of these new dimensions characterizes Cohen-Macaulay rings with dualizing ideals.

We characterize unmixed and Cohen-Macaulay edge-weighted edge ideals of very well-covered graphs. also provide examples oriented graphs that have non-Cohen-Macaulay vertex-weighted ideals, while the ideal their underlying graph is Cohen-Macaulay. This disproves a conjecture posed by Pitones, Reyes, Toledo.

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x 1 ,. .. , x n ] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi's theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and He...

We study properties of a poset generating a Cohen-Macaulay algebra with straightening laws (ASL for short). We show that if a poset P generates a Cohen-Macaulay ASL, then P is pure and, if P is moreover Buchsbaum, then P is Cohen-Macaulay. Some results concerning a Rees algebra of an ASL defined by a straightening closed ideal are also established. And it is shown that if P is a Cohen-Macaulay ...

Let G be a simple undirected graph on n vertices, and let I(G) ⊆ R = k[x1, . . . , xn] denote its associated edge ideal. We show that all chordal graphs G are sequentially Cohen-Macaulay; our proof depends upon showing that the Alexander dual of I(G) is componentwise linear. Our result complements Faridi’s theorem that the facet ideal of a simplicial tree is sequentially Cohen-Macaulay and impl...