Related papers: Unitarily graded field extensions

A fundamental tool of Differential Galois Theory is the assignment of an algebraic group to each finite-dimensional differential module over differential field in such a way that the category of differential modules it generates is…

We define generalized Koszul modules and rings and develop a generalized Koszul theory for $\mathbb{N}$-graded rings with the degree zero part noetherian semiperfect. This theory specializes to the classical Koszul theory for graded rings…

In his $1994$ survey, Kleinert defined formally and formulated the problem to obtain unit theorems for unit groups of orders in a semisimple algebra $A$. If $A$ is a group algebra $FG$, it boils down to classifying all finite groups $G$…

We prove modularity lifting theorems for l-adic Galois representations of any dimension satisfying a unitary type condition and a Fontaine-Laffaille type condition at l. This extends the results of Clozel, Harris and Taylor, and the…

We generalize results of P. Schneider and U. Stuhler for GL_l+1 to a reductive algebraic group G defined and split over a non-archimedean local field K. Following their lines, we prove that the generalized Steinberg representations of G…

Let S be a commutative ring, Q a group that acts on S, and let R be the subring of S fixed under Q. A Q-normal S-algebra consists of a central S-algebra A and a homomorphism s from Q to the group Out(A) of outer automorphisms of A that…

It was proved by Valenti and Zaicev, in 2011, that, if $G$ is an abelian group and $K$ is an algebraically closed field of characteristic zero, then any $G$-grading on the algebra of upper block triangular matrices over $K$ is isomorphic to…

For each finite subgroup $G$ of $PGL_2(\mathbb{Q})$, and for each integer $n$ coprime to $6$, we construct explicitly infinitely many Galois extensions of $\mathbb{Q}$ with group $G$ and whose ideal class group has $n$-rank at least…

One of the fundamental questions in current field theory, related to Grothendieck's conjecture of birational anabelian geometry, is the investigation of the precise relationship between the Galois theory of fields and the structure of the…

For a differential field $F$ having an algebraically closed field of constants, we analyze the structure of Picard-Vessiot extensions of $F$ whose differential Galois groups are unipotent algebraic groups and apply these results to study…

We construct a Galois correspondence for finite purely inseparable field extensions $F/K$, generalising a classical result of Jacobson for extensions of exponent one (where $x^p \in K$ for all $x\in F$).

Motivated by the work of Lubotzky, we use Galois cohomology to study the difference between the number of generators and the minimal number of relations in a presentation of the Galois group $G_S(k)$ of the maximal extension of a global…

We classify all cubic extensions of any field of arbitrary characteristic, up to isomorphism, via an explicit construction involving three fundamental types of cubic forms. We deduce a classification of any Galois cubic extension of a…

In this paper we show that a semi-commutative Galois extension of associative unital algebra by means of an element, whose Nth power is equal to the identity element of an algebra, where N is an integer greater or equal to two, induces a…

Let $A = \bigoplus_{i \geqslant 0} A_i$ be a graded locally finite $k$-algebra such that $A_0$ is an arbitrary finite-dimensional algebra satisfying some splitting condition. In this paper we develop a generalized Koszul theory generalizing…

We define a generalization $\mathfrak{G}$ of the Grassmann algebra $G$ which is well-behaved over arbitrary commutative rings $C$, even when $2$ is not invertible. In particular, this enables us to define a notion of superalgebras that does…

For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's…

We prove the universal lifting theorem: for an $\alpha$-simply connected and $\alpha$-connected Lie groupoid $\gm$ with Lie algebroid $A$, the graded Lie algebra of multi-differentials on $A$ is isomorphic to that of multiplicative…

In this note we compare the a-invariant of a homogeneous algebra B to the a-invariant of a subalgebra A. In particular we show that if $A \subset B$ is a finite homogeneous inclusion of standard graded domains over an algebraically closed…

The notion of a coalgebra-Galois extension is defined as a natural generalisation of a Hopf-Galois extension. It is shown that any coalgebra-Galois extension induces a unique entwining map $\psi$ compatible with the right coaction. For the…