Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8905254 | Bulletin des Sciences Mathématiques | 2018 | 11 Pages |
Abstract
A celebrated conjecture of Auslander and Reiten claims that a finitely generated module M that has no extensions with MâÎ over an Artin algebra Î 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.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
Olgur Celikbas, Kei-ichiro Iima, Arash Sadeghi, Ryo Takahashi,