Related papers: The structure of perfect fields
We use the "geometric axioms" point of view to give an effective listing of the complete types of the theory $DCF_{0}$ of differentially closed fields of characteristic $0$. This gives another account of observations made in earlier papers.
In this paper we examine the commutativity of ideal extensions. We introduce methods of constructing such extensions, in particular we construct a noncommutative ring T which contains a central and idempotent ideal I such that T/I is a…
We use a generalization of a construction by Ziegler to show that for any field $F$ and any countable collection of countable subsets $A_i \subseteq F, i \in \calI \subset \Z_{>0}$ there exist infinitely many fields $K$ of arbitrary…
In this paper I consider polynomial composites with the coefficients from $K\subset L$. We already know many properties, but we do not know the answer to the question of whether there is a relationship between composites and field…
We present an application of elimination theory to the study of singularities over arbitrary fields, particularly to the open problem of resolution. A partial extension of a function, defining resolution of singularities over fields of…
Many examples of rank two bundles on ${\bf P}^4$ are constructed in positive characteristic. Construction depends on constructing certain special bundles on ${\bf P}^3$ which is shown to be equivalent to constructing bundles on ${\bf P}^4$…
In this note we study one-dimensional definable sets in power series fields with perfect residue fields. Using the description of automorphisms given by Schilling, in \cite{S44}, we show that such sets are unions of existentially definable…
It is shown that physical fields are formed by physical structures, which in their properties are differential-geometrical structures. These results have been obtained due to using the mathematical apparatus of skew-symmetric differential…
We give a new and elementary proof showing that a homeomorphism of a compact metric space is positively expansive if and only if the space is finite.
Recently, it has been proved that if we have a field extension, then it has linear matching property if and only if L is purely transcendental or is an extension of prime degree. In this note we provide a counterexample for this result.
We prove an explicit upper bound on the number of real quadratic fields that admit a universal quadratic form of a given rank, thus establishing a density zero statement. More generally, we obtain such a result for totally positive definite…
A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
We obtain a necessary and sufficient condition for an algebraic set in a group to have a fully characteristic radical. As a result, we see that if the radical of a system of equation $S$ over a group $G$ is fully characteristic, then there…
The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…
Given a totally real number field $F$, we show that there are only finitely many totally real extensions of $K$ of a fixed degree that admit a universal quadratic form defined over $F$. We further obtain several explicit classification…
We study the group of automorphisms of the affine plane preserving some given curve, over any field. The group is proven to be algebraic, except in the case where the curve is a bunch of parallel lines. Moreover, a classification of the…
Certain towers of function fields with complete splitting of rational places at each stage are constructed. Also, families oof towers with positive N/g ratios are described.
This paper represents the main portion of the Ph.D. Thesis of the author, and is the first of the series of four papers, which is a joint work with K. Matsuki as a whole. We present a program toward constructing an algorithm for resolution…
Hyperstructures are a natural extension of regular algebraic structures in which one of the operations, known as the hyperoperation, is multivalued; a hyperfield is such an extension on a field. M. Krasner (1962) proved that the quotient…