Given a square-free monomial ideal $I$ in polynomial ring $R$ over field $\mathbb{K}$, one can associate it with its LCM-lattice and hypergraph. In this short note, we establish the connection between hypergraph, doing so provide sufficient condition for removing higher dimension edges of hypergraph without impacting projective ideal. We also offer algorithms to compute class ideals built using...

Let Γ be a finite graph together with a group Gv at each vertex v. The graph product G(Γ) is obtained from the free product of all Gv by factoring out by the normal subgroup generated by {ghgh; g ∈ Gv, h ∈ Gw} for all adjacent v, w. In this note we construct a projective resolution for G(Γ) given projective resolutions for each Gv, and obtain some applications. Let Γ be a finite graph together ...

We introduce the concept of edgewise domination in clutters, and use it to provide an upper bound for the projective dimension of any squarefree monomial ideal. We then compare this bound to a bound given by Faltings. Finally, we study a family of clutters associated to graphs and compute domination parameters for certain classes of these clutters.

In this paper, we give estimates of ideal or minimal distances between the distribution of the normalized partial sum and the limiting Gaussian distribution for stationary martingale difference sequences or stationary sequences satisfying projective criteria. Applications to functions of linear processes and to functions of expanding maps of the interval are given.

In this paper we introduce and investigate a class of those rings in which every projective ideal is free. We establish the transfer of this notion to the trivial ring extension and pullbacks and then generate new and original families of rings satisfying this property.

We will construct a Quillen model structure out of the multiplier ideal sheaves on a smooth quasi-projective variety using earlier works of Isaksen and Barnea and Schlank. We also show that fibrant objects of this model category are made of kawamata log terminal pairs in birational geometry.

A basis of the ideal of the complement of a linear subspace in a projective space over a finite field is given. As an application, the second largest number of points of plane curves of degree d over the finite field of q elements is also given for d ≥ q + 1.

Consider the posets PI = Borel(R) \ I where I is a σ-ideal σ-generated by a projective collection of closed sets. Then the PI extension is given by a single real r of an almost minimal degree: every real s ∈ V [r] is Cohen-generic over V or