Related papers: Formal Matrix Rings: Isomorphism Problem
We consider the groups of regular circulant matrices over finite fields and integer residue class rings. In both cases we present a formula for the order of these groups. We also make a first step towards finding the algebraic structure of…
A ring $R$ with center $C$ is said to be \textit{centrally essential} if the module $R_C$ is an essential extension of the module $C_C$. In the paper, we study groups whose group algebras over fields are centrally essential rings. We focus…
In this note, we use the isomorphism of the ring of $G$-circulant matrices over a field $k$ with the group ring $k[G]$ to derive a very short proof of the Classical Maschke Theorem.
This paper studies the unitary diagonalization of matrices over formal power series rings. Our main result shows that a normal matrix is unitarily diagonalizable if and only if its minimal polynomial completely splits over the ring and the…
In this work we give an explicit construction of the isomorphism of coefficient rings of Buchstaber and Krichever formal groups.
We study a ring containing a complete set of orthogonal idempotents as a generalized matrix ring via its Peirce decomposition. We focus on the case where some of the underlying bimodule homomorphisms are zero. Upper and lower triangular…
This paper aims at the following results: \begin{enumerate} \item The class of all $*$-regular rings forms a variety. \item A subdirectly irreducible $*$-regular ring $R$ is faithfully representable (i.e. isomorphic to a subring of an…
This article is concerned with homological properties of local or graded rings whose defining relations are monomials on some regular sequence. The main result of the article positively answers a question of Avramov for such a ring $R$.…
Rings with Nakayama permutations, pseudo-Frobenius and Frobenius rings in particular, are studied by applying the general theory of formal matrix rings to their Peirce decompositions. A combinatorial criterion is given to decide whether a…
In previous papers, the author showed that in many cases of interest there exists an isomorphism between certain path algebras related to the structure of the subregular J-rings of Coxeter systems and matrix rings over a free product of…
This is the first paper in a series that studies smooth relative Lie algebra homologies and cohomologies based on the theory of formal manifolds and formal Lie groups. In this paper, we lay the foundations for this study by introducing the…
In this paper, we introduce the upper and lower approximations on the invers set-valued mapping and the approximations an established on a powerful set valued homomorphism from a ring R1 to power sets of a ring R2. Moreover, the properties…
We study elementary equivalence of adele rings and decidability for adele rings of general number fields. We prove that elementary equivalence of adele rings implies isomorphism of the adele rings.
We give a criterium of holomorphy for some type formal power series. This gives a stronger form of a Rothstein's type extension theorem for a particular ring of holomorphic functions.
In this paper, we study the classes of rings in which every proper (regular) ideal can be factored as an invertible ideal times a nonempty product of proper radical ideals. More precisely, we investigate the stability of these properties…
In this article, we explore the problem of determining isomorphisms between the twisted complex group algebras of finite $p$-groups. This problem bears similarity to the classical group algebra isomorphism problem and has been recently…
Given an element $f$ in a regular local ring, we study matrix factorizations of $f$ with $d \ge 2$ factors, that is, we study tuples of square matrices $(\varphi_1,\varphi_2,\dots,\varphi_d)$ such that their product is $f$ times an identity…
A notion of one-dimensional formal ring is presented. It consists of a triple $(A,\Phi,\Psi)$ where $A$ is a unital ring and $\Phi$ and $\Psi$ are two formal power series in $2$ variables ${\Phi(x,y),\Psi(x,y)\in A\llbracket…
We provide a complete system of invariants for the formal classification of complex analytic unipotent germs of diffeomorphism at $\cn{n}$ fixing the orbits of a regular vector field. We reduce the formal classification problem to solve a…
We describe the pushforward of a matrix factorisation along a ring morphism in terms of an idempotent defined using relative Atiyah classes, and use this construction to study the convolution of kernels defining integral functors between…