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Mare
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Let $A=KQ/I$ be a finite dimensional connected quiver algebra with admissible ideal $I$ with n points and m arrows and $M$ an $A$-module.

Question: Is the projective dimension of $M$ bounded by $n+m$ if it is finite?

Of course it would be surprising to see a proof, but maybe there is a simple counterexample.

Let $A=KQ/I$ be a connected quiver algebra with n points and m arrows and $M$ an $A$-module.

Question: Is the projective dimension of $M$ bounded by $n+m$ if it is finite?

Of course it would be surprising to see a proof, but maybe there is a simple counterexample.

Let $A=KQ/I$ be a finite dimensional connected quiver algebra with admissible ideal $I$ with n points and m arrows and $M$ an $A$-module.

Question: Is the projective dimension of $M$ bounded by $n+m$ if it is finite?

Of course it would be surprising to see a proof, but maybe there is a simple counterexample.

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Mare
Mare
  • 26.5k
  • 6
  • 25
  • 104

Bounding the projective dimension of modules by the number of points and arrows

Let $A=KQ/I$ be a connected quiver algebra with n points and m arrows and $M$ an $A$-module.

Question: Is the projective dimension of $M$ bounded by $n+m$ if it is finite?

Of course it would be surprising to see a proof, but maybe there is a simple counterexample.