Related papers: On the radical of a monomial ideal
In recent years, the combinatorial properties of monomials ideals and binomial ideals have been widely studied. In particular, combinatorial interpretations of free resolution algorithms have been given in both cases. In this present work,…
We give a new combinatorial characterization of the big height of a squarefree monomial ideal leading to a new bound for the projective dimension of a monomial ideal.
The reduction number of monomial ideals in the polynomial $K[x,y]$ is studied. We focus on ideals $I$ for which $J=(x^a,y^b)$ is a reduction ideal. The computation of the reduction number amounts to solve linear inequalities. In some…
We prove the componentwise linearity of ideals that satisfy a certain exchange property similar to polymatroidal ideals. We also discuss the componentwise linearity and exchange properties of ideals of $k$-covers of totally balanced…
We study when Taylor resolutions of monomial ideals are minimal. We consider monomial ideals with linear quotients. In particular, we determine precisely the stable ideals and the monomial ideals with linear resolutions having the miminal…
We consider the problem of determining whether a monomial ideal is dominant. This property is critical for determining for which monomial ideals the Taylor resolution is minimal. We first analyze dominant ideals with a fixed least common…
Taking a ring-theoretic perspective as our motivation, the main aim of this series is to establish a comprehensive theory of ideals in commutative quantales with an identity element. This particular article focuses on an examination of…
The Riemann-Roch theorem on a graph G is related to Alexander duality in combinatorial commutive algebra. We study the lattice ideal given by chip firing on G and the initial ideal whose standard monomials are the G-parking functions. When…
In this work, we investigate the transfer of some homological properties from a ring $R$ to his amalgamated duplication along some ideal $I$ of $R$, and then generate new and original families of rings with these properties.
For monomial special multiserial algebras, which in general are of wild representation type, we construct radical embeddings into algebras of finite representation type. As a consequence, we show that the representation dimension of…
In this article algebraic constructions are introduced in order to study the variety defined by a radical parametrization (a tuple of functions involving complex numbers, $n$ variables, the four field operations and radical extractions). We…
A graph-theoretic method, simpler than existing ones, is used to characterize the minimal set of monomial generators for the integral closure of any algebra of polynomials generated by quadratic monomials. The toric ideal of relations…
Linear resolutions and the stronger notion of linear quotients are important properties of monomial ideals. In this paper, we fully characterize linear quotients in terms of the lcm-lattice of monomial ideals. We also formulate an analogous…
Let $R=K[x_1,...,x_n]$ be the polynomial ring in $n$ variables over a field $K$ and $I$ be a monomial ideal generated in degree $d$. Bandari and Herzog conjectured that a monomial ideal $I$ is polymatroidal if and only if all its monomial…
This is a survey of recent progress in several areas of combinatorial algebra. We consider combinatorial problems about free groups, polynomial algebras, free associative and Lie algebras. Our main idea is to study automorphisms and, more…
This paper concerns the exponentiation of monomial ideals. While it is customary for the exponentiation operation on ideals to consider natural powers, we extend this notion to powers where the exponent is a positive real number. Real…
To a simplicial complex, we associate a square-free monomial ideal in the polynomial ring generated by its vertex set over a field. We study algebraic properties of this ideal via combinatorial properties of the simplicial complex. By…
Given multigraded free resolutions of two monomial ideals we construct a multigraded free resolution of the sum of the two ideals.
We give a necessary and sufficient condition on a homogeneous polynomial ideal for its Taylor complex to be exact. Then we give a combinatorial construction of a minimal resolution for ideals satisfying the above condition (in particular…
We provide an alternative proof that the finite rational linear combination of radicals, under certain constraint, are linearly independent over $\mathbb{Q}$.