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http://dx.doi.org/10.4134/JKMS.2014.51.1.189

THE IDENTITY-SUMMAND GRAPH OF COMMUTATIVE SEMIRINGS  

Atani, Shahabaddin Ebrahimi (Faculty of Mathematical Sciences University of Guilan)
Hesari, Saboura Dolati Pish (Faculty of Mathematical Sciences University of Guilan)
Khoramdel, Mehdi (Faculty of Mathematical Sciences University of Guilan)
Publication Information
Journal of the Korean Mathematical Society / v.51, no.1, 2014 , pp. 189-202 More about this Journal
Abstract
An element r of a commutative semiring R with identity is said to be identity-summand if there exists $1{\neq}a{\in}R$ such that r+a = 1. In this paper, we introduce and investigate the identity-summand graph of R, denoted by ${\Gamma}(R)$. 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 ${\Gamma}(R)$ are studied.
Keywords
I-semiring; co-ideal; Q-strong co-ideal; co-semidomain; identity-summand graph; identity-summand element;
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Times Cited By KSCI : 2  (Citation Analysis)
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