Let J be the ideal of vertex covers of a graph G. We give a graph theoretical characterization of the minimal generators of the symbolic Rees algebra of J . If G is perfect, it is shown that the Rees algebra of J is normal and we compute the irreducible representation of the Rees cone of J in terms of cliques. Then we prove that if G is perfect and unmixed, then the Rees algebra of J is a Goren...

We show that, for an arbitrary graph, a regular ideal of the associated Leavitt path algebra is also graded. As consequence, row-finite we obtain that quotient by again and Condition (L) preserved quotients ideals. Furthermore, describe vertex set make comparison between theory ideals in algebras graph C*-algebras.

In this paper we examine some natural ideal conditions and show how graphs can be defined that give a visualization of these conditions. We the interplay between multiplicative theory graph theoretic structure associated graph. Behavior under standard ring extensions are studied, in conjunction with theory, classical results connections made.

For any countable directed graph E we describe the primitive ideal space of the corresponding generalized Cuntz-Krieger algebra C∗(E).

Each partition λ = (λ1, λ2, . . . , λn) determines a so-called Ferrers tableau or, equivalently, a Ferrers bipartite graph. Its edge ideal, dubbed a Ferrers ideal, is a squarefree monomial ideal that is generated by quadrics. We show that such an ideal has a 2-linear minimal free resolution; i.e. it defines a small subscheme. In fact, we prove that this property characterizes Ferrers graphs amo...

A tetrahedral curve is a (usually nonreduced) curve in P defined by an unmixed, height two ideal generated by monomials. We characterize when these curves are arithmetically Cohen-Macaulay by associating a graph to each curve and, using results from combinatorial commutative algebra and Alexander duality, relating the structure of the complementary graph to the Cohen-Macaulay property.

In this paper, polynomial ideal theory is used to deal with the problem of the Spacking coloring of a finite undirected and unweighted graph by introducing a family of polynomials encoding the problem. A method to find the S-packing colorings of the graph is presented and illustrated by examples.

In this paper, we present results concerning the structure of ideals in Leavitt path algebra a (countable) directed graph with coefficients an integral domain, such as, describing set generators for ideal; necessary and sufficient conditions ideal to be prime; simple. Besides, some other interesting properties are also mentioned.