相关论文: Some properties of finite meadows

The goal of these lectures is to explain speaker's results on uniqueness properties of spherical varieties. By a uniqueness property we mean the following. Consider some special class of spherical varieties. Define some combinatorial…

We say that a class of finite structures for a finite first-order signature is $r$-compressible if each structure $G$ in the class has a first-order description of size at most $O(r(|G|))$. We show that the class of finite simple groups is…

In this paper, in the first we give definitions of some classes of division rings which strictly contain the class of centrally finite division rings. One of our main purpose is to construct non-trivial examples of rings of new defined…

In this note is we exhibit an elementary method to construct explicitly curves over finite fields with many points. Despite its elementary character the method is very efficient and can be regarded as a partial substitute for the use of…

We establish a connection between finite fields and finite dynamical systems. We show how this connection can be used to shed light on some problems in finite dynamical systems and in particular, in linear systems.

We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the…

We study links between first-order formulas and arbitrary properties for families of theories, classes of structures and their isomorphism types. Possibilities for ranks and degrees for formulas and theories with respect to given properties…

We define a cell complex with an action of the even spin mapping class group, and use it to obtain a finite presentation. We also obtain a finite presentation with Dehn twist generators.

In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to…

We revisit finite racks and quandles using a perspective based on permutations which can aid in the understanding of the structure. As a consequence we recover old results and prove new ones. We also present and analyze several examples.

We investigate finite field extensions of the unital 3-field, consisting of the unit element alone, and find considerable differences to classical field theory. Furthermore, the structure of their automorphism groups is clarified and the…

We study model theory of fields with actions of a fixed finite group scheme. We prove the existence and simplicity of a model companion of the theory of such actions, which generalizes our previous results about truncated iterative…

We classify the semifields and division semirings containing the max-plus semifield $\mathbb{Z}_\mathrm{max}$, which are finitely generated as $\mathbb{Z}_\mathrm{max}$-semimodules.

In the first part of this article, we consider ruled surfaces defined over a finite field; we introduce invariants for them, and describe some explicit contructions that illustrate possible behaviour of these invariants. In the second part,…

We obtain several finiteness results for the unramified cohomology of function fields of algebraic varieties defined over fields of type (F'_m), a class that includes algebraically closed fields, finite fields, local fields, and some higher…

We investigate the theory of finite observables, i.e., resolutions of the finite-dimensional identity by means of positive operators, that have a physical interpretation in terms of measurement schemes. We focus on extremal and rank-one…

The first examples of formations which are arboreous (and therefore Hall) but not freely indexed (and therefore not locally extensible) are found. Likewise, the first examples of solvable formations which are freely indexed and arboreous…

A finite semifield is a division algebra over a finite field where multiplication is not necessarily associative. We consider here the complexity of the multiplication in small semifields and finite field extensions. For this operation, the…

Internal preneighbourhood spaces inside any finitely complete category with finite coproducts and proper factorisation structure were first introduced in my earlier paper. This paper proposes a closure operation on internal preneighbourhood…

We generalise the construction of infinite matroids from trees of matroids to allow the matroids at the nodes, as well as the field over which they are represented, to be infinite.