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Hausdorff dimension, box dimension, packing dimension and similar concepts.

32 votes
3 answers
5k views

Krull dimension less or equal than transcendence degree?

Let $k$ be a field, and $A$ a $k$-domain, so that the fraction field of $A$ has transcendence degree $n$ over $k$. If $A$ is finitely-generated over $k$, then $A$ has Krull dimension $n$ (Theorem A i …
Greg Muller's user avatar
10 votes
Accepted

Different definitions of the dimension of an algebra

In a non-commutative ring, you need to be careful with what you even mean by a prime ideal, and usually there are very few two-sided ideals you might call prime. Oh, and even in the cases when there …
Greg Muller's user avatar