Suppose $R$ is an integral domain and $R$ is algebraically closed. Prove that it then follows $R$ is a field.
How to prove that every algebraically closed integral domain is a field?
4
$\begingroup$
abstract-algebra
ring-theory
integral-domain
-
2@Mariano, how about turning these comments into an answer? – 2011-04-15
1 Answers
3
This is a community wiki answer intended to get this question off the unanswered list.
As Mariano mentions in the comments, the solution of $ax-1$ for $a\neq 0$ furnishes an inverse for $a$ in $R$.