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Let $R$ be a commutative semiring with non-zero identity. In this paper, we introduce and study the graph $Ω (R)$ 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 $Γ (R)$ and $Ω (R)$ .

On idempotent semifields and a paper by H. Hutchins.

H.J. Weinert (1983)

Semigroup forum

On injective $L$ -modules.

Isaac, Paul (2005)

International Journal of Mathematics and Mathematical Sciences

On Interassociativity and Related Questions

DAVID ZUPNIK (1971)

Aequationes mathematicae

On Jacobson radical of a $Γ$ -semiring.

Sardar, Sujit Kumar (2005)

Novi Sad Journal of Mathematics

On $k$ -ideals of semirings.

Sen, M.K., Adhikari, M.R. (1992)

International Journal of Mathematics and Mathematical Sciences

On k-radicals of Green's relations in semirings with a semilattice additive reduct

Tapas Kumar Mondal, Anjan Kumar Bhuniya (2013)

Discussiones Mathematicae - General Algebra and Applications

We introduce the k-radicals of Green's relations in semirings with a semilattice additive reduct, introduce the notion of left k-regular (right k-regular) semirings and characterize these semirings by k-radicals of Green's relations. We also characterize the semirings which are distributive lattices of left k-simple subsemirings by k-radicals of Green's relations.

On $L$ -fuzzy ideals in semirings. I

Young Bae Jun, Joseph Neggers, Hee Sik Kim (1998)

Czechoslovak Mathematical Journal

In this paper we extend the concept of an $L$ -fuzzy (characteristic) left (resp. right) ideal of a ring to a semiring $R$ , and we show that each level left (resp. right) ideal of an $L$ -fuzzy left (resp. right) ideal $μ$ of $R$ is characteristic iff $μ$ is $L$ -fuzzy characteristic.

On $L$ -fuzzy ideals in semirings. II

Joseph Neggers, Young Bae Jun, Hee Sik Kim (1999)

Czechoslovak Mathematical Journal

We study some properties of $L$ -fuzzy left (right) ideals of a semiring $R$ related to level left (right) ideals.

On left, right and two-sided cancellable elements of semigroups.

H.J. Weinert (1978)

Semigroup forum

On limits in complete semirings.

G. Karner (1992)

Semigroup forum

On linear operators strongly preserving invariants of Boolean matrices

Yizhi Chen, Xian Zhong Zhao (2012)

Czechoslovak Mathematical Journal

Let $𝔹_{k}$ be the general Boolean algebra and $T$ a linear operator on $M_{m, n} (𝔹_{k})$ . If for any $A$ in $M_{m, n} (𝔹_{k})$ ( $M_{n} (𝔹_{k})$ , respectively), $A$ is regular (invertible, respectively) if and only if $T (A)$ is regular (invertible, respectively), then $T$ is said to strongly preserve regular (invertible, respectively) matrices. In this paper, we will give complete characterizations of the linear operators that strongly preserve regular (invertible, respectively) matrices over $𝔹_{k}$ . Meanwhile, noting that a general Boolean algebra $𝔹_{k}$ is isomorphic...

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