Open AccessA note on super integral rings
Author(s) -
Rajat Kanti Nath
Publication year - 2019
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.v38i4.39637
Subject(s) - combinatorics , spec# , mathematics , commutative ring , graph , spectrum (functional analysis) , ring (chemistry) , vertex (graph theory) , center (category theory) , physics , commutative property , discrete mathematics , crystallography , computer science , chemistry , quantum mechanics , organic chemistry , programming language
Let $R$ be a nite non-commutative ring with center $Z(R)$. The commuting graph of $R$, denoted by $\Gamma_R$, is a simple undirected graph whose vertex set is $R\setminus Z(R)$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = yx$. Let$\Spec(\Gamma_R), \L-Spec(\GammaR)$ and $\Q-Spec(\GammaR)$ denote the spectrum, Laplacian spectrum and signless Laplacian spectrum of $\Gamma_R$ respectively. A nite non-commutative ring $R$ is called super integral if $\Spec(\Gamma_R), \L-Spec(Gamma_R)$ and $\Q-Spec(\Gamma_R)$ contain only integers. In this paper, we obtain several classes of super integral rings.