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Let $k$ be an algebraically closed field and $A$ be an Artin-Shelter regular $k$-algebra. Fix a numerical polynomial $H(t)$. I would like to know whether or not semi-stable f.g. graded $A$-modules with Hilbert polynomial $H(t)$ is bounded. More precisely we regard g.f. graded modules $M$ and $N$ as isomorphic is they are isomorphic up to torsion modules. Semi-stability and boundedness are defined in the same manner as commutative case.

The boundedness may not be hold for general AS regular algebras, but then I would like to know for which class of algebra this kind of boundedness result hold. I would appreciate any reference, comments and suggestion.

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