Classification of rings with toroidal Jacobson graph

Title:

Classification of rings with toroidal Jacobson graph

Creator:

Selvakumar, Krishnan and Subajini, Manoharan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:f469ffcb-edda-405a-b947-2b0bedb8c60c
uuid:f469ffcb-edda-405a-b947-2b0bedb8c60c
issn:0011-4642

Subject:

matematika, grafy funkcí, mathematics, graphs of functions, planar graph, genus of a graph, local ring, nilpotent element, Jacobson graph, 13, and 51

Type:

model:article and TEXT

Format:

print, bez média, and svazek

Description:

Let R be a commutative ring with nonzero identity and J(R) the Jacobson radical of R. The Jacobson graph of R, denoted by JR, is defined as the graph with vertex set RJ(R) such that two distinct vertices x and y are adjacent if and only if 1 − xy is not a unit of R. The genus of a simple graph G is the smallest nonnegative integer n such that G can be embedded into an orientable surface Sn. In this paper, we investigate the genus number of the compact Riemann surface in which JR can be embedded and explicitly determine all finite commutative rings R (up to isomorphism) such that JR is toroidal., Krishnan Selvakumar, Manoharan Subajini., and Obsahuje seznam literatury

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

307-316

Source:

Czechoslovak Mathematical Journal | 2016 Volume:66 | Number:2

Harvested from:

CDK

Metadata only:

false