Related papers: Small skew fields

It is proved that any supersimple field has trivial Brauer group, and more generally that any supersimple division ring is commutative. As prerequisites we prove several results about generic types in groups and fields whose theory is…

A well-known theorem of Wedderburn asserts that a finite division ring is commutative. In a division ring the group of invertible elements is as large as possible. Here we will be particularly interested in the case where this group is as…

A long-standing conjecture of Podewski states that every minimal field is algebraically closed. It was proved by Wagner for fields of positive characteristic, but it remains wide open in the zero-characteristic case. We reduce Podewski's…

We prove that two finite-dimensional commutative algebras over an algebraically closed field are isomorphic if and only if they give rise to isomorphic representations of the category of finite sets and surjective maps.

Let $T$ be a complete theory of fields, possibly with extra structure. Suppose that model-theoretic algebraic closure agrees with field-theoretic algebraic closure, or more generally that model-theoretic algebraic closure has the exchange…

Let R be an associative ring with possible extra structure. R is said to be weakly small if there are countably many 1-types over any finite subset of R. It is locally P if the algebraic closure of any finite subset of R has property P. It…

We expand our previously founded basic theory of equiresidual algebraic geometry over an arbitrary commutative field, to a well-behaved theory of (equiresidual) algebraic varieties over a commutative field, thanks to the generalisation of…

A subfield $K$ of $\bar{\mathbb{Q}}$ is $large$ if every smooth curve $C$ over $K$ with a rational point has infinitely many rational points. A subfield $K$ of $\bar{\mathbb{Q}}$ is $big$ if for every positive integer $n$, $K$ contains a…

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that…

We prove a microlocal characterisation of character sheaves on a reductive Lie algebra over an algebraically closed field of sufficiently large positive characteristic: a perverse irreducible G-equivariant sheaf is a character sheaf if and…

We study just infinite algebras which remain so upon extension of scalars by arbitrary field extensions. Such rings are called stably just infinite. We show that just infinite rings over algebraically closed fields are stably just infinite…

We show that C-minimal fields (i.e., C-minimal expansions of ACVF) have the exchange property, answering a question of Haskell and Macpherson. Additionally, we strengthen some theorems of Cubides Kovacsics and Delon on C-minimal fields.…

We show that a lattice-ordered field (not necessarily commutative) is totally ordered if and only if each square is positive, answering a generalized question of Conrad and Dauns (Pacific J. Math. 30 (1969), 385--398) in the affirmative. As…

Let G be a unitary group of a signed-Hermitian form h given over a non-Archimedian local field k of residue characteristic not two. Let V be the vector space on which h is defined. We consider minimal skew-strata, more precisely pairs (b,a)…

We show that types over real algebraically closed sets are stationary, both for the theory of separably closed fields of infinite degree of imperfection and for the theory of beautiful pairs of algebraically closed field. The proof is given…

We study the late time evolution of flat and negatively curved FRW models with a perfect fluid matter source and a scalar field having an arbitrary non-negative potential function $V(\phi) .$ We prove using a dynamical systems approach four…

We study continuous groups of generalized Kerr-Schild transformations and the vector fields that generate them in any n-dimensional manifold with a Lorentzian metric. We prove that all these vector fields can be intrinsically characterized…

We classify fields having finitely many finite non-commutative (not necessarily central) division algebras over them. In the process, we introduce the notion of anti-closure of a field and also make comments on fields having a linear…

Non(anti)commutativity in an open free superstring and also one moving in a background anti-symmetric tensor field is investigated. In both cases, the non(anti)commutativity is shown to be a direct consequence of the non-trivial boundary…

G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an…