Can Field of fractions be Algebraically Closed?

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Let R be an integral domain which isn't a field.

Can it be the case that the field of fractions is algebraically closed?

The reason I'm asking this is : The field of fractions of $\mathbb Z$ is $\mathbb Q$ which isn't algebraically closed.

One algebraic closure is C.

Is $\mathbb C$ the field of fractions of some non field integral domain?