Related papers: On graded division rings
We show that the new result on H\"older continuity of solutions to a class of nondiagonal elliptic systems with $p$-growth in [2] can be used to improve the $L^q$ theory for such systems.
Let $D$ be a division ring. In this paper, we investigate properties of subgroups of an arbitrary subnormal subgroup of the multiplicative group $D^*$ of $D$. The new obtained results generalize some previous results on subgroups of $D^*$.
We complete the description of group gradings on finite-dimensional incidence algebras. Moreover, we classify the finite-dimensional graded algebras that can be realized as incidence algebras endowed with a group grading.
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the…
We show that if two rings have equivalent derived categories then they have the same algebraic K-theory. Similar results are given for G-theory, and for a large class of abelian categories.
We develop the theory of logarithmic p-divisible groups and the theory of logarithmic finite locally free commutative group schemes.
In this paper, we consider graded near-rings over a monoid $G$ as a generalizations of graded rings over groups. We introduce certain innovative graded prime ideals and study some of its basic properties over graded near-rings.
The general theory of Grothendieck categories is presented. We systemize the principle methods and results of the theory, showing how these results can be used for studying rings and modules.
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
This paper classifies the derivations of twisted group algebras in terms of the generators and defining relations of the group. In particular, we generalize some know results over group algebras to the case of twisted group algebras. We…
In this article we show how Gr\"un's results in group theory can be used for studying the structure of class groups in normal extensions.
We generalize the idea of a Schur ring of a group to the category of semigroups. Fundamental results of Schur rings over groups are shown to be true for Schur rings over semigroups. Examples where Schur rings differ between the two…
We develop a Dieudonn\'e theory for $p$-divisible groups using sheared Witt vectors.
In this paper we introduce and study the class of graded U-nil clean rings, as a generalization of graded nil-good class defined in [3]. We also investigate the transfer of the graded U-nil cleaness to matrix rings, and to graded group…
Consider a pseudo-$H$-space $E$ endowed with a separately continuous biadditive associative multiplication which induces a grading on $E$ with respect to an abelian group $G$. We call such a space a graded pseudo-$H$-ring and we show that…
In this paper, we investigate primeness of groupoid graded rings. We provide a set of necessary and sufficient conditions for primeness of a nearly-epsilon strongly groupoid graded ring. Furthermore, we apply our main result to get a…
We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a $p$-adic field, together with relevant arithmetic information about the fields generated by the irreducible…
We generalize the constructions of [17,19] to layered semirings, in order to enrich the structure and provide finite examples for applications in arithmetic (including finite examples). The layered category theory of [19] is extended…
This paper considers graded near-rings over a monoid G as a generalizations of the graded rings over groups, introduce certain innovative graded weakly prime ideals and graded almost prime ideals as a generalizations of graded prime ideals…
A theory of graded manifolds can be viewed as a generalization of differential geometry of smooth manifolds. It allows one to work with functions which locally depend not only on ordinary real variables, but also on $\mathbb{Z}$-graded…