Related papers: A note on Galois theory for bialgebroids

In this paper motivated by the celebrated fundamental theorem of algebra and its standard proof utilizing Liouville's Theorem, we prove the fundamental theorem of algebra type results for both commutative and noncommutative polynomials in…

We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the…

In the preprint we present an outline of the one dimensional version of topological Galois theory. The theory studies topological obstruction to solvability of equations "in finite terms" (i.e. to their solvabilty by radicals, by elementary…

Let A be a basic connected finite dimensional algebra over an algebraically closed field, let G be a group, let T be a basic tilting A-module and let B the endomorphism algebra of T. Under a hypothesis on T, we establish a correspondence…

This is an introduction to double algebras which is the structure modelled by the properties of the convolution product in Hopf algebras, weak Hopf algebras and in Hopf algebroids. We show that Hopf algebroids with a Frobenius integral can…

With a small suitable modification, dropping the projectivity condition, we extend the notion of a Frobenius algebra to grant that a Frobenius algebra over a Frobenius commutative ring is itself a Frobenius ring. The modification introduced…

In this short note, we show that the cohomology of an algebra entwined with a coalgebra as defined by T. Brzezi\'nski (J. Algebra 235 (2001), no. 1, 176--202; arXiv:math.RA/9909108) computes the Hochschild cohomology of the subalgebra of…

Let $F/E$ be a finite Galois extension of fields with abelian Galois group $\Gamma$. A self-dual normal basis for $F/E$ is a normal basis with the additional property that $Tr_{F/E}(g(x),h(x))=\delta_{g,h}$ for $g,h\in\Gamma$.…

We say a tame Galois field extension $L/K$ with Galois group $G$ has trivial Galois module structure if the rings of integers have the property that $\Cal{O}_{L}$ is a free $\Cal{O}_{K}[G]$-module. The work of Greither, Replogle, Rubin, and…

This paper concerns the description of holomorphic extensions of algebraic number fields. We define a hyperbolized adele class group for every number field K Galois over Q and consider the Hardy space H[K] of graded-holomorphic functions on…

It is shown that any finite complete covering of a non-commutative algebra in the sense of Calow and Matthes (J. Geom. Phys. 32 (2000), 114--165) gives rise to a Galois coring.

In this mainly expository note, we state a criterion for when a left Kan extension of a lax monoidal functor along a strong monoidal functor can itself be equipped with a lax monoidal structure, in a way that results in a left Kan extension…

We make explicit certain results around the Galois correspondence in the context of definable automorphism groups, and point out the relation to some recent papers dealing with the Galois theory of algebraic differential equations when the…

Let D be a valued division algebra, finite-dimensional over its center F. Assume D has an unramified splitting field. The paper shows that if D contains a maximal subfield which is Galois over F (i.e. D is a crossed product) then the…

In this paper, we describe minimal presentations of maximal pro-$2$ quotients of absolute Galois groups of formally real Pythagorean fields of finite type. For this purpose, we introduce a new class of pro-$2$ groups: $\Delta$-Right Angled…

Given a number field $F$, a finite group $G$ and an indeterminate $T$, {\it{a $G$-parametric extension over $F$}} is a finite Galois extension $E/F(T)$ with Galois group $G$ and $E/F$ regular that has all the Galois extensions of $F$ with…

Let k be an algebraically closed field. Given an extension A : B of finite-dimensional k- algebras, we establish criteria ensuring that the representation-theoretic notion of polynomial growth is preserved under ascent and descent. These…

Let $H$ be a finite-dimensional weak Hopf algebra over a field $k$ and $A/B$ be a right faithfully flat weak $H$-Galois extension. We prove that if the finitistic dimension of $B$ is finite, then it is less than or equal to that of $A$.…

One way of interpreting a left Kan extension is as taking a kind of "partial colimit", whereby one replaces parts of a diagram by their colimits. We make this intuition precise by means of the "partial evaluations" sitting in the so-called…

A theorem of Paul Roberts states that the integral closure of a regular local ring in a generically abelian extension is Cohen-Macaulay, provided the characteristic of the residue field does not divide the order of the Galois group. An…