Additive Polynomials and Their Role in the Model Theory of Valued Fields
نویسنده
چکیده
We discuss the role of additive polynomials and p-polynomials in the theory of valued fields of positive characteristic and in their model theory. We outline the basic properties of rings of additive polynomials and discuss properties of valued fields of positive characteristic as modules over such rings. We prove the existence of Frobenius-closed bases of algebraic function fields F |K in one variable and deduce that F/K is a free module over the ring of additive polynomials with coefficients in K. Finally, we prove that every minimal purely wild extension of a henselian valued field is generated by a p-polynomial.
منابع مشابه
Additive Polynomials over Perfect Fields
where aij ∈ K. Additive polynomials over valued fields in positive characteristic play an important role in understanding many algebraic and model theoretic properties of maximal fields of positive characteristic, see [7] for a thorough examination of the issue. A subset S of a valued field (K, v) has the optimal approximation property if for all a ∈ K, the set {v(s − a) : s ∈ S} has a maximal ...
متن کاملNotes on extremal and Tame Valued Fields
We extend the characterization of extremal valued fields given in [1] to the missing case of valued fields of mixed characteristic with perfect residue field. This leads to a complete characterization of the tame valued fields that are extremal. The key to the proof is a model theoretic result about tame valued fields in mixed characteristic. Further, we prove that in an extremal valued field o...
متن کاملA Multi Objective Graph Based Model for Analyzing Survivability of Vulnerable Networks
In the various fields of disaster management, choosing the best location for the Emergency Support & Supply Service Centers (ESSSCs) and the survivability of the network that provides the links between ESSSCs and their environment has a great role to be paid enough attention. This paper introduces a graph based model to measure the survivability of the linking's network. By values computed for ...
متن کاملGENERALIZED FUZZY VALUED $theta$-Choquet INTEGRALS AND THEIR DOUBLE-NULL ASYMPTOTIC ADDITIVITY
The generalized fuzzy valued $theta$-Choquet integrals will beestablished for the given $mu$-integrable fuzzy valued functionson a general fuzzy measure space, and the convergence theorems ofthis kind of fuzzy valued integral are being discussed.Furthermore, the whole of integrals is regarded as a fuzzy valuedset function on measurable space, the double-null asymptoticadditivity and pseudo-doub...
متن کاملExploring the Use of Random Regression Models withLegendre Polynomials to Analyze Clutch Sizein Iranian Native Fowl
Random regression models (RRM) have become common for the analysis of longitudinal data or repeated records on individual over time. The goal of this paper was to explore the use of random regression models with orthogonal / Legendre polynomials (RRL) to analyze new repeated measures called clutch size (CS) as a meristic trait for Iranian native fowl. Legendre polynomial functions of increasing...
متن کامل