On the Mulitplicity of Zeros of Polynomials over Arbitrary Finite Dimensional K-Algebras.
On the multiplicity of .
On the Noether exponent
We obtain, in a simple way, an estimate for the Noether exponent of an ideal I without embedded components (i.e. we estimate the smallest number μ such that ).
On the Nonflatness of Analytic Tensor Product.
On the nontrivial solvability of systems of homogeneous linear equations over in ZFC
Motivated by the paper by H. Herrlich, E. Tachtsis (2017) we investigate in ZFC the following compactness question: for which uncountable cardinals , an arbitrary nonempty system of homogeneous -linear equations is nontrivially solvable in provided that each of its subsystems of cardinality less than is nontrivially solvable in ?
On the non-vanishing of cotangent cohomology.
On the non-vanishing of local cohomology modules
It is shown that for any Artinian modules , is the greatest integer such that .
On the notions of characteristics and type for modules and their applications
On the number of compatibly Frobenius split subvarieties, prime -ideals, and log canonical centers
Let be a projective Frobenius split variety with a fixed Frobenius splitting . In this paper we give a sharp uniform bound on the number of subvarieties of which are compatibly Frobenius split with . Similarly, we give a bound on the number of prime -ideals of an -finite -pure local ring. Finally, we also give a bound on the number of log canonical centers of a log canonical pair. This final variant extends a special case of a result of Helmke.
On the Number of Faces of Simplicial Complexes and the Purity of Frobenius.
On the number of generators of modules over Laurent Rings.
On the number of generators of modules over polynomial affine rings.
On the partial Euler-Poincare characteristics of certain systems of parameters in local rings.
On the Pierce-Birkhoff Conjecture for Smooth Affine Surfaces over Real Closed Fields
We will prove that the Pierce-Birkhoff Conjecture holds for non-singular two-dimensional affine real algebraic varieties over real closed fields, i.e., if is such a variety, then every piecewise polynomial function on can be written as suprema of infima of polynomial functions on . More precisely, we will give a proof of the so-called Connectedness Conjecture for the coordinate rings of such varieties, which implies the Pierce-Birkhoff Conjecture.
On the Poincaré series associated to the p-adic points on a curve
On the Poincaré series for a plane divisorial valuation.
On the Polynomial Ring over a Mori Domain
On the polynomial-like behaviour of certain algebraic functions
Given integers and a constant , consider the space of -tuples of real polynomials in variables of degree , whose coefficients are in absolute value, and satisfying . We study the family of algebraic functions, where is a polynomial, and being a constant depending only on . The main result is a quantitative extension theorem for these functions which is uniform in . This is used to prove Bernstein-type inequalities which are again uniform with respect to .The proof is based on...
On the Prime Ideal of an Ordering of Higher Level.
On the product of a module by an ideal