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

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 …

We study unmixed and Cohen-Macaulay properties of the binomial edge ideal of some
classes of graphs. We compute the depth of the binomial edge ideal of a generalized block …

We characterize all pairs of graphs $(G_1, G_2) $, for which the binomial edge ideal $ J_
{G_1, G_2} $ has linear relations. We show that $ J_ {G_1, G_2} $ has a linear resolution if …

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We characterize all graphs whose binomial edge ideals have pure resolutions. Moreover,
we introduce a new switching of graphs which does not change some algebraic invariants of …

We consider determinantal ideals, where the generating minors are encoded in a
hypergraph. We study when the generating minors form a Gröbner basis. In this case, the …

Let G be a simple graph on n vertices and JK m, G be the generalized binomial edge ideal of
G in S= K [xi, j: i∈[m], j∈[n]]. We give a regularity upper bound of S/JK m, G. We prove that …

Herzog, Hibi, Hreindóttir et al. introduced the class of closed graphs, and they proved that
the binomial edge ideal JG of a graph G has quadratic Gröbner bases if G is closed. In this …

This paper analyzes the cohomological dimension of the generalized binomial edge ideal
$\calJ_ {K_m, G} $ for a complete $ r $-partite graph $ G $. Additionally, the Krull dimension …