Historically, commutative algebra, whose foundations were laid by Dedekind, Hilbert,
Noether, and Krull, has developed in step with algebraic geometry, number theory …

The v-number of a graded ideal is an algebraic invariant introduced by Cooper et al., and
originally motivated by problems in algebraic coding theory. In this paper we study the case …

The Castelnuovo–Mumford regularity of binomial edge ideals - ScienceDirect Skip to main
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We relate homological properties of a binomial edge ideal $\mathcal {J} _G $ to invariants
that measure the connectivity of a simple graph $ G $. Specifically, we show if $ R/\mathcal …

Inspired by work of Cartwright and Sturmfels, in [15] we introduced two classes of
multigraded ideals named after them. These ideals are defined in terms of properties of their …

In this article, we obtain an upper bound for the Castelnuovo-Mumford regularity of powers
of an ideal generated by a homogeneous quadratic sequence in a polynomial ring in terms …

Let JG be the binomial edge ideal of a graph G. We characterize all graphs whose binomial
edge ideals, as well as their initial ideals, have regularity 3. Consequently we characterize …

Let G be a simple graph on n vertices. Let LG and IG denote the Lovász–Saks–Schrijver
(LSS) ideal and parity binomial edge ideal of G in the polynomial ring S= K [x 1,…, xn, y 1 …

We study the Betti numbers of binomial edge ideal associated to some classes of graphs
with large Castelnuovo-Mumford regularity. As an application we give several lower bounds …

Let $ G $ be a finite simple graph and let $ I_G $ denote its associated toric ideal in the
polynomial ring $ R $. For each integer $ n\geq 2$, we completely determine all the possible …