Comaximal graph of commutative rings

dc.creatorMaimani, Hamid Reza
dc.creatorSalimi, Maryam
dc.creatorSattari, Asiyeh
dc.creatorYassemi, Siamak
dc.date2007-01-31
dc.date.accessioned2026-07-07T07:44:05Z
dc.date.available2026-07-07T07:44:05Z
dc.descriptionLet $R$ be a commutative ring with identity. Let $Γ(R)$ be a graph with vertices as elements of $R$, where two distinct vertices $a$ and $b$ are adjacent if and only if $Ra+Rb=R$. In this paper we consider a subgraph $Γ_2(R)$ of $Γ(R)$ which consists of non-unit elements. We look at the connectedness and the diameter of this graph. We completely characterize the diameter of the graph $Γ_2(R)\setminus\J(R)$. In addition, it is shown that for two finite semi-local rings $R$ and $S$, if $R$ is reduced, then $Γ(R)\congΓ(S)$ if and only if $R\cong S$.
dc.description8 Pages
dc.identifierhttps://arxiv.org/abs/math/0701918
dc.identifierhttp://arxiv.org/abs/math/0701918
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123066
dc.subjectCommutative Algebra
dc.subjectCombinatorics
dc.subject05C75; 13A15
dc.titleComaximal graph of commutative rings
dc.typetext

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