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Results tagged with ac.commutative-algebra
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user 2330
Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics.
14
votes
2
answers
8k
views
Choosing the algebraic independent elements in Noether's normalization lemma
Given a field $k$ and a finitely generated $k$-algebra $R$ without zero divisors, one knows that there exist $x_1, \ldots, x_n$ algebraically independent such that $R$ is integral over $k[x_1, \ldots, …
- 1,320
23
votes
6
answers
6k
views
Noether's normalization lemma over a ring A
Given a field $k$ and a finitely generated $k$-algebra $R$ without zero divisors, one knows that there exist $x_1, \ldots, x_n$ algebraically independent such that $R$ is integral over $k[x_1, \ldots, …
- 1,320
12
votes
4
answers
7k
views
Definition of étale for rings
Let $A \to B$ be a ring extension.
What is the definition of $B/A$ étale ?
When $A$ is a field, do we get a nice characterization ?
- 1,320
29
votes
3
answers
7k
views
Non finitely-generated subalgebra of a finitely-generated algebra
Ok, I feel a little bit ashamed by my question.
This afternoon in the train, I looked for a counter-example:
— $k$ a field
— $A$ a finitely generated $k$-algebra
— $B$ a $k$-subalgebra of $A$ that …