Morita Invariance of the Filter Dimension and of the Inequality of Bernstein

@article{Bavula2006MoritaIO,
  title={Morita Invariance of the Filter Dimension and of the Inequality of Bernstein},
  author={V. Bavula and V. Hinchcliffe},
  journal={Algebras and Representation Theory},
  year={2006},
  volume={11},
  pages={497-504}
}
It is proved that the filter dimension is Morita invariant. A direct consequence of this fact is the Morita invariance of the inequality of Bernstein: if an algebra A is Morita equivalent to the ring ${\cal D} (X)$ of differential operators on a smooth irreducible affine algebraic variety X of dimension n ≥ 1 over a field of characteristic zero then the Gelfand–Kirillov dimension $ {\rm GK} (M)\geq n = \frac{{\rm GK} (A)}{2}$ for all nonzero finitely generated A-modules M. In fact, a stronger… Expand
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References

SHOWING 1-8 OF 8 REFERENCES
Cherednik algebras and differential operators on quasi-invariants
  • 121
  • Highly Influential
  • PDF
Filter Dimension
  • 5
  • PDF
Krull, Gelfand–Kirillov, and Filter Dimensions of Simple Affine Algebras☆
  • 9
  • PDF
Noncommutative Noetherian Rings
  • 1,589
Commutative rings of partial differential operators and Lie algebras
  • 144
  • Highly Influential
Filter dimension of algebras and modules, a simplicity criterion of generalized weyl algebras
  • 21