Levelled O-minimal structures.
We introduce the notion of leveled structure and show that every structure elementarily equivalent to the real expo field expanded by all restricted analytic functions is leveled.
Lifting -modules from positive to zero characteristic
We study liftings or deformations of -modules ( is the ring of differential operators from EGA IV) from positive characteristic to characteristic zero using ideas of Matzat and Berthelot’s theory of arithmetic -modules. We pay special attention to the growth of the differential Galois group of the liftings. We also apply formal deformation theory (following Schlessinger and Mazur) to analyze the space of all liftings of a given -module in positive characteristic. At the end we compare the problems...
Limites uniformes de polynômes dans un corps valué complet non archimédien
Linear dependence of zeros of polynomials and construction of primitve elements.
Linear derivations with rings of constants generated by linear forms
Let k be a field. We describe all linear derivations d of the polynomial algebra k[x₁,...,xₘ] such that the algebra of constants with respect to d is generated by linear forms: (a) over k in the case of char k = 0, (b) over in the case of char k = p > 0.
Linear differential equations and Hurwitz series
In this article, we study solutions of linear differential equations using Hurwitz series. We first obtain explicit recursive expressions for solutions of such equations and study the group of differential automorphisms of the solutions. Moreover, we give explicit formulas that compute the group of differential automorphisms. We require neither that the underlying field be algebraically closed nor that the characteristic of the field be zero.
Linear independence in linear rings with abstract differentiation
Linear operators in local fields of prime characteristic.
Linear quadratic control. State space vs. polynomial equations
Linear relations between roots of polynomials
Lineare Abhängigkeit von Wurzeln
Lineare Abhängigkeiten von Einheitswurzeln.
Linearly Reducible Difference Operators (Short Communication)
Linearly Reducible Linear Difference Operators
Line-hyperline pairs of projective spaces and fundamental subgroups of linear groups.
L'invariant de Witt de la forme Tr(x2).
Liouvillian first integrals of differential equations
In this paper we generalize to any dimension and codimension some theorems about existence of Liouvillian solutions or first integrals proved by M. Singer in Liouvillian first integrals of differential equations (1992) for first order differential equations.
Local derivations for quotient and factor algebras of polynomials
We describe all Kadison algebras of the form , where k is an algebraically closed field and S is a multiplicative subset of k[t]. We also describe all Kadison algebras of the form k[t]/I, where k is a field of characteristic zero.
Local derivations in polynomial and power series rings
We give a description of all local derivations (in the Kadison sense) in the polynomial ring in one variable in characteristic two. Moreover, we describe all local derivations in the power series ring in one variable in any characteristic.
Local global theorems for diagonal forms of higher degree.