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arXiv · 1610.04784

On the ideal case of a conjecture of Auslander and Reiten

Olgur Celikbas·Kei-ichiro Iima·Arash Sadeghi·Ryo Takahashi
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Abstract

A celebrated conjecture of Auslander and Reiten claims that a finitely generated module $M$ that has no extensions with $M\oplus \Lambda$ over an Artin algebra $\Lambda$ must be projective. This conjecture is widely open in general, even for modules over commutative Noetherian local rings. Over such rings, we prove that a large class of ideals satisfy the extension condition proposed in the aforementioned conjecture of Auslander and Reiten. Along the way we obtain a new characterization of regularity in terms of the injective dimensions of certain ideals.

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Olgur Celikbas, Kei-ichiro Iima, Arash Sadeghi, Ryo Takahashi. 2016-10-15. On the ideal case of a conjecture of Auslander and Reiten. https://arxiv.org/abs/1610.04784

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