Related papers: The core of ideals in arbitrary characteristic
We characterize the groups isomorphic to full automorphism groups of ordered abelian groups. The result will follow from classical theorems on ordered groups adding an argument from proofs used to realize rings as endomorphism rings of…
We consider complete intersection ideals in a polynomial ring over a field of characteristic zero that are stable under the action of the symmetric group permuting the variables. We determine the possible representation types for these…
We obtain explicit upper bounds for the number of irreducible factors for a class of compositions of polynomials in several variables over a given field. In particular, some irreducibility criteria are given for this class of compositions…
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…
We determine in an explicit way the depth of the fiber cone and its relation ideal for classes of monomial ideals in two variables. These classes include concave and convex ideals as well as symmetric ideals.
If $I$ is a monomial ideal with linear quotients, then it has componentwise linear quotients. However, the converse of this statement is an open question. In this paper, we provide two classes of ideals for which the converse of this…
Let R be a nil ring. We prove that primitive ideals in the polynomial ring R[x] in one indeterminate over R are of the form I[x] for some ideals I of R.
We propose a classification of group properties according to whether they can be deduced from the assumption that a group's subgroup lattice contains an interval isomorphic to some lattice. We are able to classify a few group properties as…
The generalized test ideals introduced in [HY] are related to multiplier ideals via reduction to characteristic p. In addition, they satisfy many of the subtle properties of the multiplier ideals, which in characteristic zero follow via…
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 prove the existence of infinite dense free sets (in the usual topology) for set mappings on the reals, under reasonable assumptions.
We compute the depth and regularity of ideals associated with arbitrary fillings of positive integers to a Young diagram, called the tableau ideals.
Model theoretic results such as Characterization and Definability give important information about different logics. It is well known that the proofs of those results for several modal logics have, somehow, the same 'taste'. A general proof…
We give a numerical characterization of the possible extremal Betti numbers (values as well as positions) of any homogeneous ideal in a polynomial ring over a field.
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
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…
We introduce and study varions notions of completeness of translation-invariant ideals in groups.
In this paper we show that an arbitrary solution of one ordinary difference equation is also a solution for a hierarchy of integrable difference equations. We also provide an example of such a solution that is related to sequence generated…
We prove a formula for special L-values of Anderson's modules, analogue in positive characteristic of the class number formula. We apply this result to two kinds of L-series.
In this paper, we aim to introduce and study the notion of Endo-prime hyperideals.