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http://dx.doi.org/10.5666/KMJ.2012.52.1.91

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

Darani, Ahmad Yousefian (Department of Mathematics, University of Mohaghegh Ardabili)
Publication Information
Kyungpook Mathematical Journal / v.52, no.1, 2012 , pp. 91-97 More about this Journal
Abstract
Let $R$ be a commutative semiring. We define a proper ideal $I$ of $R$ to be 2-absorbing (resp., weakly 2-absorbing) if $abc{\in}I$ (resp., $0{\neq}abc{\in}I$) implies $ab{\in}I$ or $ac{\in}I$ or $bc{\in}I$. We show that a weakly 2-absorbing ideal $I$ with $I^3{\neq}0$ 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 $R$ and study the relationship among these classes of ideals of $R$.
Keywords
Semiring; 2-absorbing ideal; Weakly 2-absorbing ideal;
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Times Cited By KSCI : 1  (Citation Analysis)
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