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edited Mar 28, 2011 at 23:22

Behaviour of Primes under Regular Coefficient Extensions

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. Does every prime ideal of the first ring expand to a prime ideal in the second?

asked Mar 28, 2011 at 22:36

user12940