Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings

  • Received : 2011.02.28
  • Accepted : 2011.09.23
  • Published : 2012.03.23
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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 $R$.

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  5. On n-absorbing ideals and (m,n)-closed ideals in trivial ring extensions of commutative rings pp.1793-6829, 2018, https://doi.org/10.1142/S0219498819501238
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