Related papers: On the intersection of principal ideals in functio…
We are interested in the structure of almost complete intersection ideals of grade 3. We give three constructions of these ideals and their free resolutions: one from the commutative algebra point of view, an equivariant construction giving…
We consider the problem of finding the minimal number of points required to intersect all lines in an affine space over the finite field of order 3. We also consider the problem of finding the minimal number of points required to intersect…
Ideals of continuous functions which satisfy an off diagonality condition proved to be important connected with the solution of large classes of nonlinear PDEs, and more recently, in General Relativity and Quantum Gravity. Maximal ideals…
In this paper we present new ways to construct external subsets of nonstandard models of arithmetic using mostly internal sets, and show that if an ultraproduct of prime finite fields includes a copy of the algebraic real numbers then…
We present an algorithm to compute a primary decomposition of an ideal in a polynomial ring over the integers. For this purpose we use algorithms for primary decomposition in polynomial rings over the rationals resp. over finite fields, and…
Let $(A,\mathfrak{m})$ be an abstract complete intersection and let $P$ be a prime ideal of $A$. In [1] Avramov proved that $A_P$ is an abstract complete intersection. In this paper we give an elementary proof of this result.
This paper is devoted to give all the technical constructions and definitions that will lead to the construction of an algorithm of resolution of singularities for binomial ideals. We construct a resolution function that will provide a…
After sketching the basic theory of injective ideals of homogeneous polynomials, we characterize injective polynomial ideals by means of a domination property and applications of this characterization to some classical operator ideals and…
A subspace arrangement in a vector space is a finite collection of vector subspaces. Similarly, a configuration of linear spaces in a projective space is a finite collection of linear subspaces. In this paper we study the degree 2 part of…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
We consider homogeneous binomial ideals $I=(f_1,\ldots,f_n)$ in $K[x_1, \ldots, x_n]$, where $f_i = a_i x_i^{d_i} - b_i m_i$ and $a_i \neq 0$. When such an ideal is a complete intersection, we show that the monomials which are not divisible…
The interpolation of couples of separable Hilbert spaces with a function parameter is studied. The main properties of the classic interpolation are proved. Some applications to the interpolation of isotropic H\"ormander spaces over a closed…
We develop the theory of central ideals on commutative rings. We introduce and study the central seminormalization of a ring in another one. This seminormalization is related to the theory of regulous functions on real algebraic varieties.…
Our main result is that possibly some non-null set of reals cannot be divided to uncountably many non-null sets. We deal also with a non-null set of reals, the graph of any function from it is null and deal with our iterations somewhat more…
We consider the operation of intersecting with a locally principal Cartier divisor (i.e., a Cartier divisor which is principal on some neighborhood of its support). We describe this operation explicitly on the level of cycles and rational…
Set-theoretical, physical, and intuitive notions of continuum are compared. It is shown that the independence of the continuum hypothesis determines status and properties of the set of intermediate cardinality. The intermediate set is a…
In this paper we study the consequences of overinterpolation, i.e., the situation when a function can be interpolated by polynomial, or rational, or algebraic functions in more points that normally expected. We show that in many cases such…
We prove that the log canonical thresholds of a large class of binomial ideals, such as complete intersection binomial ideals and the defining ideals of space monomial curves, are computable by linear programming.
The paper discuss the limit point concept of a subset in a group via ideal of the power set ring. This idea along with anti-ideal give the topological structure in a group. Homomorphic images of both ideal and anti-ideal are played the…
The core of an ideal is defined as the intersection of all of its reductions. In this paper we provide an explicit description for the core of a monomial ideal $I$ satisfying certain residual conditions, showing that ${\rm core}(I)$…