Abstract
In [1], Anderson and Badawi conjecture that every n-absorbing ideal of a commutative ring is strongly n-absorbing. In this article we prove their conjecture in certain cases (in particular this is the case for commutative algebras over an infinite field). We also show that an affirmative answer to another conjecture in [1] implies the Anderson-Badawi Conjecture.
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References
D. F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra, 39 (2011), 1646–1672.
A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75 (2007), 417–429.
P.-J. Cahen, M. Fontana, S. Frisch and S. Glaz, Open problems in commutative ring theory, Commutative Algebra: Recent Advances in Commutative Rings, Integer-Valued Polynomials and Polynomial Functions, Springer (2014), 353–375.
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Donadze, G. The Anderson-Badawi conjecture for commutative algebras over infinite fields. Indian J Pure Appl Math 47, 691–696 (2016). https://doi.org/10.1007/s13226-016-0194-3
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DOI: https://doi.org/10.1007/s13226-016-0194-3