Let $R$ be an Artin algebra and let $0 \to A \to B \to C \to 0$ be an Auslander-Reiten sequence of finitely generated left $R$-modules. Is it always true that the projective cover of $B$ equals to the direct sum of the projective cover of $A$ and the projective cover of $C$? Thank you very much.
Auslander-Reiten sequence and projective covers
Jianrong Li
- 6.2k
- 2
- 21
- 34