Related papers: Some remarks on Borel type ideals

We show that the regularity of monomial ideals whose associated prime ideals are totally ordered by inclusion is linearly bounded.

We express the Partial regularities and $a^*$-invariants of a Borel type ideal in terms of its irredundant irreducible decomposition. In addition we consider the behaviours of those invariants under intersections and sums.

We introduce a new class of monomial ideals, called strong Borel type ideals, and we compute the Mumford-Castelnouvo regularity for principal strong Borel type ideals. Also, we describe the d-fixed ideals generated by powers of variables…

In this paper, we extend a result of Eisenbud-Reeves-Totaro in the frame of ideals of Borel type.

In this paper, we extend a result of Eisenbud-Reeves-Totaro in the frame of ideals of Borel type. As a consequence, we obtain a linear upper bound for the regularity of a new class of ideals, called $\mathcal D$-fixed ideals.

For any Borel ideal we characterize ideal equal Baire system generated by the families of continuous and quasi-continuous functions, i.e., the families of ideal equal limits of sequences of continuous and quasi-continuous functions.

We introduce the notion of Q-Borel ideals: ideals which are closed under the Borel moves arising from a poset Q. We study decompositions and homological properties of these ideals, and offer evidence that they interpolate between Borel…

In this paper we use some results related to regularity, Betti numbers and reduction of generic initial ideals, showing their stability in passing from an ideal to its initial ideal if the last has some simple properties.

We bring a precision to our cited work concerning the notion of "Borel measures", as the choice among different existing definitions impacts on the validity of the results.

In this article, we characterize both Lusin's theorem and the existence of Borel representatives via the regularity properties of the measure in general topological measure spaces. As a corollary, we prove that Borel regularity of the…

In this paper, we introduce a new class of monomial ideals, called $d$-fixed ideals, which generalize the class of $p$-Borel ideals and show how some results for $p$-Borel ideals can be transfered to this new class. In particular, we give…

In this paper, we give new characterizations of algebraic regularity by using differential forms and difference quotients.

Several numerical indices that control the normalization of ideals are introduced and some relationships among them are derived.

We give sharp bounds for the Stanley depth of a special class of ideals of Borel type.

We introduce the notion of Burch ideals and Burch rings. They are easy to define, and can be viewed as generalization of many well-known concepts, for example integrally closed ideals of finite colength and Cohen--Macaulay rings of minimal…

New title and minor adjustments. To appear in the Journal of Pure and Applied Algebra

In this paper, we study various properties of matroidal ideals.

After a short review of the historical milestones on normal numbers, we introduce the Borel numbers as the reals admitting a probability function on their different bases representations. In this setting, we provide two probabilistic…

We prove formulas for the core of ideals that apply in arbitrary characteristic.

We determine the Hilbert series of some classes of ideals generated by generic forms of degree two and three, and investigate the difference to the Hilbert series of ideals generated by powers of linear generic forms of the corresponding…