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

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;

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, $\small{y{\in}R}$, the vertices x and y are adjacent if and only if $\small{xy{\in}S(I)}$.
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
Cited by
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