Related papers: The core of ideals in arbitrary characteristic
We record a general asymptotic formula for colon of ideals and proceed to give some applications regarding $m$-full, weakly $m$-full, and full ideals.
The core of an ideal is the intersection of all its reductions. We describe the core of a zero-dimensional monomial ideal I as the largest monomial ideal contained in a general reduction of I. This provides a new interpretation of the core…
We determine sets of elements which, under certain conditions, generate an intersection of ideals up to radical.
Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and…
We update Sunley's explicit estimate for the ideal-counting function, which is the number of integral ideals of bounded norm in a number field.
In this article we show how the Dedekind-Hasse criterion may be applied to prove a simple result about quadratic number fields that usually is derived as a consequence of the theory of ideals and ideal classes.
Following work of Musta\c{t}\u{a} and Bitoun we recently developed a notion of Bernstein-Sato roots for arbitrary ideals, which is a prime characteristic analogue for the roots of the Bernstein-Sato polynomial. Here we prove that for…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
We introduce the concept of constructible ideal and we relate this concept with the notion of constructible simplicial complex. Several properties of constructible ideals are studied.
In this paper, we consider the N-pure notion. An ideal $I$ of a ring $R$ is said to be N-pure, if for every $a\in I$ there exists $b\in I$ such that $a(1-b)\in N(R)$, where N(R) is nil radical of $R$. We provide new characterizations for…
For the family of graded lattice ideals of dimension 1, we establish a complete intersection criterion in algebraic and geometric terms. In positive characteristic, it is shown that all ideals of this family are binomial set theoretic…
We investigate the structure of ideals generated by binomials (polynomials with at most two terms) and the schemes and varieties associated to them. The class of binomial ideals contains many classical examples from algebraic geometry, and…
We give an explicit description of cubic rings over a discrete valuation ring, as well as a description of all ideals of such rings.
In this paper we give a unified approach for several results concerning the fiber cone of ideals
In this paper, we introduce the concept of f-ideals and discuss its algebraic properties. In particular, we give the characterization of all the f-ideals of degree 2.
We prove that the lattice of ideals of an arbitrary $L$-algebra is distributive. As a consequence, a spectral theory applies with no restriction. We also study the spectrum (i.e. the set of prime ideals) of $L$-algebras and characterize…
We prove the decidability of the elementary theory of a free group.
We study existence and computability of finite bases for ideals of polynomials over infinitely many variables. In our setting, variables come from a countable logical structure A, and embeddings from A to A act on polynomials by renaming…
Ideals are used to define homological functors for additive categories. In abelian categories the ideals corresponding to the usual universal objects are principal, and the construction reduces, in a choice dependent way, to homology…
In this paper we study the index of reducibility of powers of a standard parameter ideal. An explicit formula is proved for the extremely case. We apply the main result to compute Hilbert polynomials of socle ideals of standard parameter…