Rings in which every 2-absorbing ideal is prime

Rings in which every 2-absorbing ideal is prime

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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Veröffentlicht in:Beiträge zur Algebra und Geometrie 2018-06, Vol.59 (2), p.391-396
Hauptverfasser: Bennis, Driss, Fahid, Brahim
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Algebraic Geometry
Convex and Discrete Geometry
Geometry
Mathematics
Mathematics and Statistics
Original Paper
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Zusammenfassung: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 .
ISSN:0138-4821
2191-0383
DOI:10.1007/s13366-017-0366-2