On graph associated to co-ideals of commutative semirings

Yahya Talebi; Atefeh Darzi

Commentationes Mathematicae Universitatis Carolinae (2017)

  • Volume: 58, Issue: 3, page 293-305
  • ISSN: 0010-2628

Abstract

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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 ) .

How to cite

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Talebi, Yahya, and Darzi, Atefeh. "On graph associated to co-ideals of commutative semirings." Commentationes Mathematicae Universitatis Carolinae 58.3 (2017): 293-305. <http://eudml.org/doc/294127>.

@article{Talebi2017,
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 $\Omega (R)$.},
author = {Talebi, Yahya, Darzi, Atefeh},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {semiring; co-ideal; maximal co-ideal},
language = {eng},
number = {3},
pages = {293-305},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On graph associated to co-ideals of commutative semirings},
url = {http://eudml.org/doc/294127},
volume = {58},
year = {2017},
}

TY - JOUR
AU - Talebi, Yahya
AU - Darzi, Atefeh
TI - On graph associated to co-ideals of commutative semirings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2017
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 58
IS - 3
SP - 293
EP - 305
AB - 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 $\Omega (R)$.
LA - eng
KW - semiring; co-ideal; maximal co-ideal
UR - http://eudml.org/doc/294127
ER -

References

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