Let $K\hookrightarrow K'$ be a regular extension of fields, and $K[x_{1},\cdots,x_{n}]\hookrightarrow K'[x_{1},\cdots,x_{n}]$ the corresponding ring extension. Do every prime ideal of the first ring expands to a prime ideal in the second?
Behaviour of Primes under Regular Coefficient Extensions
user12940
- 125
- 4