Krull Dimension of A Module
If R is a commutative ring, and M is an R-module, we define the Krull dimension of M to be the Krull dimension of the quotient of R making M a faithful module. That is, we define it by the formula:
where, the annihilator, is the kernel of the natural map of R into the ring of -linear endomorphisms on .
In the language of schemes, finite type modules are interpreted as coherent sheaves, or generalized finite rank vector bundles.
Read more about this topic: Krull Dimension
Famous quotes containing the word dimension:
“God cannot be seen: he is too bright for sight; nor grasped: he is too pure for touch; nor measured: for he is beyond all sense, infinite, measureless, his dimension known to himself alone.”
—Marcus Minucius Felix (2nd or 3rd cen. A.D.)