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Let P be a lattice polytope with $h^*$-vector $(1, h^*_1, h^*_2)$. In this note we show that if $h_2^* leq h_1^*$, then $P$ is IDP. More generally, we show the corresponding statements for semi-standard graded Cohen-Macaulay domains over algebraically closed fields.
Let $D$ be a weighted oriented graph, whose underlying graph is $G$, and let $I(D)$ be its edge ideal. If $G$ has no $3$-, $5$-, or $7$-cycles, or $G$ is K{o}nig, we characterize when $I(D)$ is unmixed. If $G$ has no $3$- or $5$-cycles, or $G$ is Kon
Scattered over the past few years have been several occurrences of simplicial complexes whose topological behavior characterize the Cohen-Macaulay property for quotients of polynomial rings by arbitrary (not necessarily squarefree) monomial ideals. T
Let $(A,mathfrak{m})$ be a Henselian Cohen-Macaulay local ring and let CM(A) be the category of maximal Cohen-Macaulay $A$-modules. We construct $T colon CM(A)times CM(A) rightarrow mod(A)$, a subfunctor of $Ext^1_A(-, -)$ and use it to study propert
Let C be a uniform clutter and let I=I(C) be its edge ideal. We prove that if C satisfies the packing property (resp. max-flow min-cut property), then there is a uniform Cohen-Macaulay clutter C1 satisfying the packing property (resp. max-flow min-cu
Let $(A,mathfrak{m})$ be a hypersurface ring with dimension $d$, and $M$ a MCM $A-$module with reduction no.2 and $mu(M)=2$ or $3$ then we have proved that depth$G(M)geq d-mu(M)+1$. If $e(A)=3$ and $mu(M)=4$ then in this case we have proved that dept