-extremal valued fields.
-semiring pairs
We develop a general axiomatic theory of algebraic pairs, which simultaneously generalizes several algebraic structures, in order to bypass negation as much as feasible. We investigate several classical theorems and notions in this setting including fractions, integral extensions, and Hilbert's Nullstellensatz. Finally, we study a notion of growth in this context.
2-D polynomial equations
2-transitiv abstract ovals of odd order.
A certain property of polynomials.
A certain property of polynomials. (Short Communication).
A Characterization of Linear Difference Equations Which are Solvable by Elementary Operations.
A characterization of locally compact fields II
A characterization of locally compact fields, III
A characterization of locally compact fields of zero characteristic
A Characterization of One-Element p-Bases of Rings of Constants
Let K be a unique factorization domain of characteristic p > 0, and let f ∈ K[x₁,...,xₙ] be a polynomial not lying in . We prove that is the ring of constants of a K-derivation of K[x₁,...,xₙ] if and only if all the partial derivatives of f are relatively prime. The proof is based on a generalization of Freudenburg’s lemma to the case of polynomials over a unique factorization domain of arbitrary characteristic.
A characterization of the spherically complete normed spaces with a distinguished basis
A class of hyperrings and hyperfields.
A complete parametriziation of cyclic field extensions of 2-power degree.
A Concept of Bernoulli Numbers in Algebraic Function Fields (II).
A Condition for a Polynomial Map to be Invertible.
A conjecture in the arithmetic theory of differential equations
A constructive Approach to Noether's Problem.
A continuous, constructive solution to Hilbert's 17th problem.
A counterexample to a conjecture of multinomial degree