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Jianrong Li
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Auslander-Reiten sequence and projective covers

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.

Jianrong Li
  • 6.2k
  • 2
  • 21
  • 34