On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings

• Journal title : Kyungpook mathematical journal
• Volume 52, Issue 1,  2012, pp.91-97
• Publisher : Department of Mathematics, Kyungpook National University
• DOI : 10.5666/KMJ.2012.52.1.91
Title & Authors
On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings

Abstract
Let $\small{R}$ be a commutative semiring. We define a proper ideal $\small{I}$ of $\small{R}$ to be 2-absorbing (resp., weakly 2-absorbing) if $\small{abc{\in}I}$ (resp., $\small{0{\neq}abc{\in}I}$) implies $\small{ab{\in}I}$ or $\small{ac{\in}I}$ or $\small{bc{\in}I}$. We show that a weakly 2-absorbing ideal $\small{I}$ with $\small{I^3{\neq}0}$ is 2-absorbing. We give a number of results concerning 2-absorbing and weakly 2-absorbing ideals and examples of weakly 2-absorbing ideals. Finally we de ne the concept of 0 - (1-, 2-, 3-)2-absorbing ideals of $\small{R}$ and study the relationship among these classes of ideals of $\small{R}$.
Keywords
Semiring;2-absorbing ideal;Weakly 2-absorbing ideal;
Language
English
Cited by
1.
On weakly n-absorbing subtractive ideals in semirings, Asian-European Journal of Mathematics, 2016, 1750063
2.
On 2-Absorbing Quasi-Primary Ideals in Commutative Rings, Communications in Mathematics and Statistics, 2016, 4, 1, 55
3.
On (m,n)-closed ideals of commutative rings, Journal of Algebra and Its Applications, 2017, 16, 01, 1750013
4.
On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring, Kyungpook mathematical journal, 2016, 56, 1, 107
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