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...

We provide a generalization of pseudo-Frobenius numbers numerical semigroups to the context simplicial affine semigroups. In this way, we characterize Cohen-Macaulay type semigroup ring K[S]. define S, type(S), in terms some Apéry sets S and show that it coincides with ring, when K[S] is Cohen-Macaulay. If d-dimensional embedding dimension at most d+2, then type(S)?2. Otherwise, type(S) might b...

We describe the structure of monoid natural-valued monotone functions on an arbitrary poset. For this we provide a presentation, characterization prime elements, and description its convex hull. also study associated ring, proving that it is normal, thus Cohen-Macaulay. determine Cohen-Macaulay type, characterize Gorenstein property, Gröbner basis defining ideal. Then apply these results to qua...