On graph associated to co-ideals of commutative semirings

[摘要] 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 $\\Omega(R)$.

[学科分类] 物理化学和理论化学

[关键词] semiring;co-ideal;maximal co-idealDOI: DOI 10.14712/1213-7243.2015.219AMS Subject Classification: 16Y60 05C75 PDF