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