Abstract:Let $R$ be a commutative semiring with non-zero identity. In this paper, we introduce and study the graph $\Omega(R)$ whose vertices are all elements of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if the product of the co-ideals generated by $x$ and $y$ is $R$. Also, we study the interplay between the graph-theoretic properties of this graph and some algebraic properties of semirings. Finally, we present some relationships between the zero-divisor graph $\Gamma(R)$ and $\Omega(R)$.
Keywords: semiring; co-ideal; maximal co-ideal
DOI: DOI 10.14712/1213-7243.2015.219
AMS Subject Classification: 16Y60 05C75