Rings in which every 2-absorbing ideal is prime

Original Paper


We are interested in rings where all 2-absorbing ideals are prime. We call such class of rings 2-AB rings. In this paper, we give a characterization of 2-AB rings, for example, we show that an integral valuation domain R is a 2-AB domain if and only if \(P^2 = P\) for every prime ideal P of R.


2-Absorbing ideal Prime ideal 

Mathematics Subject Classification

13A15 13F30 


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Copyright information

© The Managing Editors 2017

Authors and Affiliations

  1. 1.Faculty of Sciences, Centre de Recherche de Mathématiques et Applications de Rabat (CeReMAR)Mohammed V University in RabatRabatMorocco

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