# What is the normalization in the Noether normalization lemma?

As I understand it, the normalization of a domain $A$ is its integral closure in its field of fractions.

Why do we call the Noether normalization lemma by that name? What ring is being normalized?

Geometrically Noether Normalization means that for any irreducible projective variety $X$ there is a finite map $\phi:X→ℙ^n$. In a sense, this helps to obtain a normalization of a variety, which is an attempt to make things nice by assuming integrally closeness. Here are some links about this: