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On graph associated to co-ideals of commutative semirings

Yahya Talebi, Atefeh Darzi (2017)

Commentationes Mathematicae Universitatis Carolinae

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 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 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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