Related papers: Revisiting Kneser's Theorem for Field Extensions

Martin Kneser proved the following addition theorem for every abelian group $G$. If $A,B \subseteq G$ are finite and nonempty, then $|A+B| \ge |A+K| + |B+K| - |K|$ where $K = \{g \in G \mid g+A+B = A+B \}$. Here we give a short proof of…

We construct a Galois correspondence for finite purely inseparable field extensions $F/K$, generalising a classical result of Jacobson for extensions of exponent one (where $x^p \in K$ for all $x\in F$).

Hilbert's Theorem 90 is a classical result in the theory of cyclic extensions. The quadratic case of Hilbert 90, however, generalizes in noncyclic directions as well. Informed by a poem of Richard Wilbur, the article explores several…

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

We extend the Heine-Stieltjes Theorem to concern all (non-degenerate) differential operators preserving the property of having only real zeros. This solves a conjecture of B. Shapiro. The new methods developed are used to describe intricate…

The Hohenberg-Kohn (HK) theorems of bijectivity between the external scalar potential and the gauge invariant nondegenerate ground state density, and the consequent Euler variational principle for the density, are proved for arbitrary…

Let $B\subset A$ be a left or right bounded extension of finite dimensional algebras. We use the Jacobi-Zariski long nearly exact sequence to show that $B$ satisfies Han's conjecture if and only if $A$ does, regardless if the extension…

The domain of convergence of a Heun function obtained through the Poincar\'{e}--Perron (P--P) theorem is not absolute convergence but conditional one [2]. We show that a uniqueness theorem is not available if we apply the P--P theorem into…

We prove that, for every $n \geq 5$, the Hasse norm principle holds for a degree $n$ extension $K/k$ of number fields with normal closure $F$ such that $\operatorname{Gal}(F/k) \cong A_n$. We also show the validity of weak approximation for…

We generalize Rado's extension theorem to complex spaces.

In a classical Hamiltonian theory with second class constraints the phase space functions on the constraint surface are observables. We give general formulas for extended observables, which are expressions representing the observables in…

Our main goal in this article is to prove a new extension theorem for sections of the canonical bundle of a weakly pseudoconvex K\"ahler manifold with values in a line bundle endowed with a possibly singular metric. We also give some…

A recent result of Balandraud shows that for every subset S of an abelian group G, there exists a non trivial subgroup H such that |TS| <= |T|+|S|-2 holds only if the stabilizer of TS contains H. Notice that Kneser's Theorem says only that…

In this article, we prove several transfer principles for the cohomological dimension of fields. Given a fixed field $K$ with finite cohomological dimension $\delta$, the two main ones allow to: - construct totally ramified extensions of…

In this paper, we use counting theorems from the geometry of numbers to extend the Riemann-Roch theorem and the Riemann-Hurwitz formula to global fields of arbitrary characteristic.

We prove an extension theorem for effective plt pairs $(X,S+B)$ of non-negative Kodaira dimension $\kappa (K_X+S+B)\geq 0$. The main new ingredient is a refinement of the Ohsawa-Takegoshi $L^2$ extension theorem involving singular hermitian…

We propose a new approach to the Fourier restriction conjectures. It is based on a discretization of the Fourier extension operators in terms of quadratically modulated wave packets. Using this new point of view, and by combining natural…

Let $G$ be one of the classical groups of Lie rank $l$. We make a similar construction of a general extension field in differential Galois theory for $G$ as E. Noether did in classical Galois theory for finite groups. More precisely, we…

In this paper, we give some extensions of K\"onig's extension of the Mazur-Orlicz theorem. These extensions include generalizations of a surprising recent result of Sun Chuanfeng, and generalizations to the product of more than two spaces…

Ando's theorem states that any pair of commuting contractions on a Hilbert space can be dilated to a pair of commuting unitaries. Parrott presented an example showing that an analogous result does not hold for a triple of pairwise commuting…