On zeros of reciprocal polynomials of odd degree.
One generalization of quasifield
One the existence of fields with few discrete valuations.
Opérateurs différentiels et courbes elliptiques
Opérateurs hypergéométriques réductibles : décompositions et groupes de Galois différentiels
Opération de Cartier et vecteurs de Witt
Ordered fields.
Ordered fields and sign-changing polynomials.
Ordered fields and the ultrafilter theorem
We prove that on the basis of ZF the ultrafilter theorem and the theorem of Artin-Schreier are equivalent. The latter says that every formally real field admits a total order.
Ordered Rings and Fields
We introduce ordered rings and fields following Artin-Schreier’s approach using positive cones. We show that such orderings coincide with total order relations and give examples of ordered (and non ordered) rings and fields. In particular we show that polynomial rings can be ordered in (at least) two different ways [8, 5, 4, 9]. This is the continuation of the development of algebraic hierarchy in Mizar [2, 3].
Ordering Epic R-Fields
Orderings under field extensions.
Ordinary linear differential equations - a survey of the global theory
Ordre de transcendance sur
Ordres faibles et localisation de zéros de polynômes
Orthogonal representations of Galois groups, Stiefel-Whitney classes and Hasse-Witt invariants.
Orthogonality and complementation in the lattice of subspaces of a finite vector space
We investigate the lattice of subspaces of an -dimensional vector space over a finite field with a prime power together with the unary operation of orthogonality. It is well-known that this lattice is modular and that the orthogonality is an antitone involution. The lattice satisfies the chain condition and we determine the number of covers of its elements, especially the number of its atoms. We characterize when orthogonality is a complementation and hence when is orthomodular. For...
Orthonormal bases for spaces of continuous and continuously differentiable functions defined on a subset of Zp.
Let K be a non-Archimedean valued field which contains Qp, and suppose that K is complete for the valuation |·|, which extends the p-adic valuation. Vq is the closure of the set {aqn | n = 0,1,2,...} where a and q are two units of Zp, q not a root of unity. C(Vq --> K) (resp. C1(Vq --> K)) is the Banach space of continuous functions (resp. continuously differentiable functions) from Vq to K. Our aim is to find orthonormal bases for C(Vq --> K) and C1(Vq --> K).
Ostrwoski's theorem for Henselian valued skew fields.
Overdetermined Strata in General Families of Polynomials
2000 Mathematics Subject Classification: 12D10.In the paper we give different examples of overdetermined strata.