Related papers: Extending maps to profinite completions in finitel…
We study projective completions of affine algebraic varieties which are given by filtrations, or equivalently, 'degree like functions' on their rings of regular functions. For a quasifinite polynomial map P (i.e. with all fibers finite) of…
Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…
Let $X$ be a quasi-affine algebraic variety isomorphic to the complement of a closed subvariety of dimension at most $n-3$ in $\C^n$. We find some conditions under which an isomorphism of two closed subvarieties of $X$ can be extended to an…
We exhibit an analogy between the problem of pushing forward measurable sets under measure preserving maps and linear relaxations in combinatorialoptimization. We show how invariance of hyperfiniteness of graphings under local isomorphism…
The $\lambda$-perfect maps, a generalization of perfect maps (continuous closed maps with compact fibers) are presented. Using $P_\lambda$-spaces and the concept of $\lambda$-compactness some results regarding $\lambda$-perfect maps will be…
We prove that if $B\subseteq A$ is an extension of finite dimensional algebras such that the projective dimension of $A/B$ as a $B$-bimodule is finite, if $A$ has finite finitistic dimension, then so does $B$. We exhibit examples…
Associative algebras with involution over a field of zero characteristic are considered. It is proved that in this case for any finitely generated associative algebra with involution there exists a finite dimensional algebra with involution…
We begin the study of completeness of affine connections, especially those on statistical manifolds as well as on affine hypersurfaces. We collect basic facts, prove new theorems and provide examples with remarkable properties.
Suppose that $\pi \: Y \to X$ is a finite map of normal varieties over a perfect field of characteristic $p > 0$. Previous work of the authors gave a criterion for when Frobenius splittings on $X$ (or more generally any $p^{-e}$-linear map)…
The problem of bi-equivariant extension of continuous maps of binary $G$-spaces is considered. The concept of a structural map of distributive binary $G$-spaces is introduced, and a theorem on the bi-equivariant extension of structural maps…
In this note we discuss some arithmetic and geometric questions concerning self maps of projective algebraic varieties.
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the…
We prove that persistently finite algebras are not created by completions of algebras, in any ordered discriminator variety. A persistently finite algebra is one without infinite simple extensions. We prove that finite measurable relation…
We explore the geometric notion of prolongations in the setting of computational algebra, extending results of Landsberg and Manivel which relate prolongations to equations for secant varieties. We also develop methods for computing…
Inversion of various inclusions, that characterize continuity in topological spaces, results in numerous variants of quotient and perfect maps. In the framework of convergences, the said inclusions are no longer equivalent, and each of them…
Permutation rational functions over finite fields have attracted high interest in recent years. However, only a few of them have been exhibited. This article studies a class of permutation rational functions constructed using trace maps on…
Quasi-Boolean algebras were introduced as the generalization of Boolean algebras in the setting of quantum computation logic. In this paper, we investigate the completeness and congruences of quasi-Boolean algebras. First, we discuss the…
Recently there has been a lot of research and progress in profinite groups. We survey some of the new results and discuss open problems. A central theme is decompositions of finite groups into bounded products of subsets of various kinds…
We give characterizations of unital uniform topological algebras and saturated locally multiplicatively convex algebras by means of multiplicative linear functionals. Some automatic continuity theorems in advertibly complete uniform…
We consider the problem of constructing a weakly-continuous mapping extending continuous mapping defined on a dense set of a topological space to the entire space. Theorem on necessary and sufficient conditions for the existence of such an…