TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL

- Journal title : Journal of the Korean Mathematical Society
- Volume 52, Issue 1, 2015, pp.159-176
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/JKMS.2015.52.1.159

Title & Authors

TOTAL IDENTITY-SUMMAND GRAPH OF A COMMUTATIVE SEMIRING WITH RESPECT TO A CO-IDEAL

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

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

Abstract

Let R be a semiring, I a strong co-ideal of R and S(I) the set of all elements of R which are not prime to I. In this paper we investigate some interesting properties of S(I) and introduce the total identity-summand graph of a semiring R with respect to a co-ideal I. It is the graph with all elements of R as vertices and for distinct x, , the vertices x and y are adjacent if and only if .

Keywords

strong co-ideal;total identity-summand graph;identity-summand graph based a co-ideal;total identity-summand graph based a co-ideal;

Language

English

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