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ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

  • Badawi, Ayman ;
  • Tekir, Unsal ;
  • Yetkin, Ece
  • Received : 2014.03.18
  • Published : 2015.01.01

Abstract

Let R be a commutative ring with $1{\neq}0$. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, $c{\in}R$ and $0{\neq}abc{\in}I$, then $ab{\in}I$ or $ac{\in}\sqrt{I}$ or $bc{\in}\sqrt{I}$. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.

Keywords

primary ideal;weakly primary ideal;prime ideal;weakly prime ideal;2-absorbing ideal;n-absorbing ideal;weakly 2-absorbing ideal;2-absorbing primary ideal;weakly 2-absorbing primary ideal

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