Related papers: Revisiting Kneser's Theorem for Field Extensions

This paper introduces the Higman-Neumann-Neumann extension (HNN extension; for short) for Nijenhuis Lie algebras and provides an embedding theorem. To this end, we employ the theory of Gr\"obner-Shirshov basis for Lie {\Omega}-algebras in…

The extended electrodynamic theory introduced by Aharonov and Bohm (after an earlier attempt by Ohmura) and recently developed by Van Vlaenderen and Waser, Hively and Giakos, can be re-written and solved in a simple and effective way in the…

In this note we extend duality theorems for crossed products obtained by M. Koppinen and C. Chen from the case of a base field or a Dedekind domain to the case of an arbitrary noetherian commutative ground ring under fairly weak conditions.…

In this paper we are concerned with the space of tempered ultrahyperfunctions corresponding to a proper open convex cone. A holomorphic extension theorem (the version of the celebrated edge of the wedge theorem) will be given for this…

In this paper we show the Hasse principle for the Brauer group of a purely transcendental extension field in one variable over an arbitrary field.

Let $(K, \nu)$ be a valued field, the notions of \emph{augmented valuation}, of \emph{limit augmented valuation} and of \emph{admissible family} of valuations enable to give a description of any valuation $\mu$ of $K [x]$ extending $\nu$.…

In this note, we prove a conjecture of Puder on an extension of the co-growth formula to any non-negative function defined on a bi-regular tree. A key component of our proof is the establishment of a resolvent identity, which serves as an…

Johnson and Lindenstrauss proved that any Lipschitz mapping from an $n$-point subset of a metric space into Hilbert space can be extended to the whole space, while increasing the Lipschitz constant by a factor of $O(\sqrt{\log n})$. We…

We consider the problem of solvability of linear differential equations over a differential field~$K$. We introduce a class of special differential field extensions, which widely generalizes the classical class of extensions of differential…

Addition theorems are principal tools that express a function $f (\bm{r} \pm \bm{r}')$ in terms of products of other functions that only depend on either $\bm{r}$ or $\bm{r}'$. The best known example of such an addition theorem is the…

We study the distribution of extensions of a number field $k$ with fixed abelian Galois group $G$, from which a given finite set of elements of $k$ are norms. In particular, we show the existence of such extensions. Along the way, we show…

In this Letter we extend the proof, by Faraco and Lindberg, of Taylor's conjecture in multiply connected domains to cover arbitrary vector potentials and remove the need to impose conditions on the magnetic field due to gauge invariance.…

The purpose of this note is to generalize the celebrated Ran and Reurings fixed point theorem to the setting of a space with a binary relation that is only transitive (and not necessarily a partial order) and a relation-complete metric. The…

We first exhibit counterexamples to some open questions related to a theorem of Sakai. Then we establish an extension theorem of Sakai type for separately holomorphic/meromorphic functions.

In this paper we will establish a structure theorem concerning the extension of analytic objects associated to germs of dimension one foliations on surfaces, through one-dimensional barriers. As an application, an extension theorem for…

The problem of extending derivations of a field $F$ to an $F-$algebra $B$ is widely studied in commutative algebra and non-commutative ring theory. For example, every derivation of $F$ extends to $B$ if $B$ is a separable algebraic…

We prove a monodromy theorem for local vector fields belonging to a sheaf satisfying the unique continuation property. In particular, in the case of admissible regular sheaves of local fields defined on a simply connected manifold, we…

In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.

The ruled residue theorem characterises residue field extensions for valuations on a rational function field. Under the assumption that the characteristic of the residue field is different from $2$ this theorem is extended here to function…

Kummer's Conjecture predicts the rate of growth of the relative class numbers of cyclotomic fields of prime conductor. We extend Kummer's Conjecture to cyclotomic fields of conductor n, where n is any natural number. We show that the…