THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGS

- Journal title : Journal of the Korean Mathematical Society
- Volume 51, Issue 1, 2014, pp.189-202
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2014.51.1.189

Title & Authors

THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGS

Atani, Shahabaddin Ebrahimi; Hesari, Saboura Dolati Pish; Khoramdel, Mehdi;

Atani, Shahabaddin Ebrahimi; Hesari, Saboura Dolati Pish; Khoramdel, Mehdi;

Abstract

An element r of a commutative semiring R with identity is said to be identity-summand if there exists such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by . It is the (undirected) graph whose vertices are the non-identity identity-summands of R with two distinct vertices joint by an edge when the sum of the vertices is 1. The basic properties and possible structures of the graph are studied.

Keywords

I-semiring;co-ideal;Q-strong co-ideal;co-semidomain;identity-summand graph;identity-summand element;

Language

English

Cited by

1.

TOTAL GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO IDENTITY-SUMMAND ELEMENTS,;;;

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