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Rings in which every 2-absorbing ideal is prime

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Abstract

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.

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Authors and Affiliations

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

    Driss Bennis & Brahim Fahid

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  1. Driss Bennis
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  2. Brahim Fahid
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Correspondence to Driss Bennis.

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Bennis, D., Fahid, B. Rings in which every 2-absorbing ideal is prime. Beitr Algebra Geom 59, 391–396 (2018). https://doi.org/10.1007/s13366-017-0366-2

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  • DOI: https://doi.org/10.1007/s13366-017-0366-2

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