Related papers: Isomorphisms between Jacobson graphs

We give a survey of some recent results on the fusion semirings of compact quantum groups (computations of and applications to discrete quantum groups) by using the following simplifying terminology: we say that a compact quantum group G is…

We prove that we have an isomorphism of type $A_{aut}(\mathbb C_\sigma[G])\simeq A_{aut}(\mathbb C[G])^\sigma$, for any finite group $G$, and any 2-cocycle $\sigma$ on $G$. In the particular case $G=\mathbb Z_n^2$, this leads to a…

For an artinian ring $R$, the directed zero-divisor graph $\Gamma(R)$ is connected if and only if there is no proper one-sided identity element in $R$. Sinks and sources are characterized and clarified for finite ring $R$, especially, it is…

Let $R$ and $S$ be commutative rings with identity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$…

In this paper, we introduce a new class of rings calling them {\it 2-UNJ rings}, which generalize the well-known 2-UJ, 2-UU and UNJ rings. Specifically, a ring $R$ is called 2-UNJ if, for every unit $u$ of $R$, the inclusion $u^2 \in 1 +…

Let $M$ be a graph manifold such that each piece of its JSJ decomposition has the $\Bbb H^2 \times \Bbb R$ geometry. Assume that the pieces are glued by isometries. Then, there exists a complete Riemannian metric on $\Bbb R \times M$ which…

We prove that the group of automorphisms of the generic meet-tree expansion of an infinite non-unary free Fra\"{\i}ss\'{e} limit over a finite relational language is simple. As a prototypical case, the group of automorphism of the Rado…

We introduce two remarkable identities written in terms of single commutators and anticommutators for any three elements of arbitrary associative algebra. One is a consequence of other (fundamental identity). From the fundamental identity,…

In this note we provide a negative answer to the question: ``Is it true that for every positive rational number $r$ there exists a finite abelian group $G$ such that $|\mathrm{Aut}(G)|/|G| = r$?". We show that if $r = a/b$ is a rational…

A ring R is called an E-ring if the canonical homomorphism from R to the endomorphism ring End(R_Z) of the additive group R_Z, taking any r in R to the endomorphism left multiplication by r turns out to be an isomorphism of rings. In this…

The goal of this paper is to construct and describe certain arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph $\Gamma$ we construct an arithmetic subgroup…

We define a generalized Jacobian $\mathrm{J}_\mathfrak{m}(\mathit{Gr})$ and a generalized Picard group $\mathrm{P}_\mathfrak{m}(\mathit{Gr})$ of a graph $\mathit{Gr}$ with respect to a modulus $ \mathfrak{m}=\sum_{i=1}^s m_iw_i$ with $w_i$…

Recall that an element $x\in R$ is {\bf complemented} if there is a $y\in R$ such that $xy = 0$ and $x + y \in {\rm reg}(R)$. In a recent article [1], the authors investigated those rings for which every non-nilpotent element is…

Let $R$ be a finite commutative ring with unity $1_R$ and $k \in R$. Properties of one-sided $k$-orthogonal $n \times n$ matrices over $R$ are presented. When $k$ is idempotent, these matrices form a semigroup structure. Consequently new…

Let $Aut_{alg}(X)$ be the subgroup of the group of regular automorphisms $Aut(X)$ of an affine algebraic variety $X$ generated by all connected algebraic subgroups. We prove that if $dim X \ge 2$ and if $Aut_{alg}(X)$ is rich enough,…

This paper studies the co-maximal graph $\Om(R)$, the induced subgraph $\G(R)$ of $\Om(R)$ whose vertex set is $R\setminus (U(R)\cup J(R))$ and a retract $\G_r(R)$ of $\G(R)$, where $R$ is a commutative ring. We show that the core of…

A subgroup Q is commensurated in a group G if each G conjugate of Q intersects Q in a group that has finite index in both Q and the conjugate. So commensurated subgroups are similar to normal subgroups. Semistability and simple connectivity…

A finite graph $\G$ is said to be {\em $(G,3)$-$($connected$)$ homogeneous} if every isomorphism between any two isomorphic (connected) subgraphs of order at most $3$ extends to an automorphism $g\in G$ of the graph, where $G$ is a group of…

For any graph inverse semigroup $G(E)$ we describe subsemigroups $D^0=D\cup\{0\}$ and $J^0=J\cup\{0\}$ of $G(E)$ where $D$ and $J$ are arbitrary $\mathcal{D}$-class and $\mathcal{J}$-class of $G(E)$, respectively. In particular, we prove…

Let the join of two graphs be the union of two disjoint graphs connected by $j$ edges in a one-to-one manner. In previous work by Gyurov and Pinzon, which generalized the results of Badura and Rara, the determinant of the adjacency matrix…