A proof of the Anderson–Badawi \( \mathbf{rad}\varvec{(I)}^{\varvec{n}} \varvec{\subseteq } {\varvec{I}}\) formula for \(\varvec{n}\)-absorbing ideals

  • Guram Donadze


In [1], Anderson and Badawi conjectured that \(\mathrm{rad}(I)^n \subseteq I\) for every n-absorbing ideal I of a commutative ring. In this article, we prove their conjecture. We also prove related conjectures for radical ideals.


n-Absorbing ideal strongly n-absorbing ideal 

2010 Mathematics Subject Classification

13A15 13F05 13G05 


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Copyright information

© Indian Academy of Sciences 2018

Authors and Affiliations

  1. 1.Indian Institute of Science Education and ResearchThiruvananthapuramIndia

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