Related papers: Embeddings of fields in simple algebras over globa…

Let $K$ be a global function field together with a place $\infty$, and $A$ the subring of functions regular outside $\infty$. In this paper we present an effective method to evaluate the (locally free) class number of an arbitrary…

Any algebra herein is intended over a field of characteristic 0. Let $E$ denote the infinite dimensional Grassman algebra. Given a power associative finite dimensional {$\mathbb{Z}_2$-graded-central-simple} $A$ and a supertrace algebra $B$,…

Let K be a local non-archimedian field, F=K((t)) and let G be a split semi-simple group. The purpose of this paper is to study certain analogs of spherical (and Iwahori) Hecke algebras for representations of the group G(F) and its central…

We investigate the failure of a local-global principle with regard to "containment of number fields"; i.e., we are interested in pairs of number fields $(K_1,K_2)$ such that $K_2$ is not a subfield of any algebraic conjugate $K_1^\sigma$ of…

Let $k$ be a field containing an algebraically closed field of characteristic zero. If $G$ is a finite group and $D$ is a division algebra over $k$, finite dimensional over its center, we can associate to a faithful $G$-grading on $D$ a…

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…

Let K be a complete discretely valued field with residue field k and F be a function field of a curve over K. Let L/F be a Galois extension of degree n. If n is coprime to char(k), then under some assumptions on k(e.g. k is algebraically…

It is shown that a separable exact residually finite dimensional C*-algebra with locally finitely generated (rational) even K-homology embeds in a uniformly hyperfinite C*-algebra.

Let $K$ be a complete discretely valued field with the residue field $\kappa$. Assume that cohomological dimension of $\kappa$ is less than or equal to $1$ (for example, $\kappa$ is an algebraically closed field or a finite field). Let $F$…

This note is purely expository. In the course of the Kolmogorov-Arnold solution of Hilbert's 13th problem on superpositions there appeared the notion of basic embedding. A subset K of R^2 is basic if for each continuous function f:K->R…

By a result of Orlov there always exists an embedding of the derived category of a finite-dimensional algebra of finite global dimension into the derived category of a high-dimensional smooth projective variety. In this article we give some…

We introduce a notion of embedding codimension of an arbitrary local ring, establish some general properties, and study in detail the case of arc spaces of schemes of finite type over a field. Viewing the embedding codimension as a measure…

An integral quadratic lattice is called indefinite $k$-universal if it represents all integral quadratic lattices of rank $k$ for a given positive integer $k$. For $k\geq 3$, we prove that the indefinite $k$-universal property satisfies the…

Let $\mathbb{F}$ be a field and $\mathsf{G}$ a group. This work is inspired in the following problem: "{\it given a division (simple) $\mathsf{G}$-graded $\mathbb{F}$-algebra, is there any other division (simple) $\mathsf{G}$-graded…

We investigate when a computable automorphism of a computable field can be effectively extended to a computable automorphism of its (computable) algebraic closure. We then apply our results and techniques to study effective embeddings of…

We prove that the arithmetic degree of a graded or local ring is bounded above by the arithmetic degree of any of its associated graded rings with respect to ideals $I$ in $A$. In particular, if $Spec (A)$ is equidimensional and has an…

This paper considers K\"{o}the's question of whether every associative locally finite-dimensional (abbr., LFD) central division algebra $R$ over a field $K$ is a normally locally finite (abbr., NLF) algebra over $K$, that is, whether every…

Suppose that a complex manifold M is locally embedded into a higher-dimensional neighbourhood as a submanifold. We show that, if the local neighbourhood germs are compatible in a suitable sense, then they glue together to give a global…

We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and…

Let $G$ be a linear algebraic group over a field $k$ of characteristic 0. We show that any two connected semisimple $k$-subgroups of $G$ that are conjugate over an algebraic closure of $k$ are actually conjugate over a finite field…