Self-injective commutative rings have no nontrivial rigid ideals
H Lindo - arXiv preprint arXiv:1710.01793, 2017 - arxiv.org
arXiv preprint arXiv:1710.01793, 2017•arxiv.org
… We establish a link between trace modules and rigidity in modules over Noetherian rings.
Using the theory of trace ideals we make partial progress on a question of Dao, and on the
Auslander-Reiten conjecture over Artinian Gorenstein rings. … Recall that we say a left R-module
M is rigid if Ext1 R(M,M) = 0 and that a commutative Noetherian ring is Artinian Gorenstein if
and only if it is self-injective. …
Using the theory of trace ideals we make partial progress on a question of Dao, and on the
Auslander-Reiten conjecture over Artinian Gorenstein rings. … Recall that we say a left R-module
M is rigid if Ext1 R(M,M) = 0 and that a commutative Noetherian ring is Artinian Gorenstein if
and only if it is self-injective. …
We establish a link between trace modules and rigidity in modules over Noetherian rings. Using the theory of trace ideals we make partial progress on a question of Dao, and on the Auslander-Reiten conjecture over Artinian Gorenstein rings.
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