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Seelakant6vr

Answered question

2022-02-14

Simple question about finitely generated algebras
I have two finitely generated algebras A and B over a field K such that

B \subseteq A

. Is it true that

A = B [a_{1}, \dots, a_{n}]

for some

a_{1}, \dots, a_{n} \in A

?

Answer & Explanation

Nathen Wilkerson

Beginner2022-02-15Added 4 answers

If A is finitely generated over K then we have

A = K [a_{1}, \dots, a_{n}]

for some elements

a_{1}, \dots, a_{n} \in A

.
Then:

A = K [a_{1}, \dots, a_{n}] \subseteq B [a_{1}, \dots, a_{n}] \subseteq A

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