2 results
FP-injective dimensions and Gorenstein homology
- Part of
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- Journal:
- Proceedings of the Edinburgh Mathematical Society / Volume 65 / Issue 4 / November 2022
- Published online by Cambridge University Press:
- 21 December 2022, pp. 1183-1199
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Let $R$
be a left coherent ring. It is proven that if an $R$
-module $M$
has a finite FP-injective dimension, then the Gorenstein projective (resp. Gorenstein flat) dimension and the projective (resp. flat) dimension coincide. Also, we obtain that the pair ($\mathcal {GP},\, \mathcal {GP}^{\perp }$
) forms a projective cotorsion pair under some mild conditions.
PROGRESS ON THE AUSLANDER–REITEN CONJECTURE
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 93 / Issue 3 / June 2016
- Published online by Cambridge University Press:
- 16 March 2016, pp. 433-440
- Print publication:
- June 2016
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- Article
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Let
$R$ be a commutative Gorenstein ring. A result of Araya reduces the Auslander–Reiten conjecture on the vanishing of self-extensions to the case where 
$R$ has Krull dimension at most one. In this paper we extend Araya’s result to certain 
$R$-algebras. As a consequence of our argument, we obtain examples of bound quiver algebras that satisfy the Auslander–Reiten conjecture.
