This is probably an easy question, but I'm not able to figure it out.

Are the following the same:

1. Field of fractions of the Witt ring over the algebraic closure of $\mathbb{F}_p$

2. Algebraic closure of the field of p-adics (which is the field of fractions of the Witt ring over $\mathbb{F}_p$)

In other words, does the operation of taking the field of fractions of the Witt ring commute with the operation of taking the algebraic closure?

This is probably an easy question, but I'm not able to figure it out.

Are the following the same:

1. Field of fractions of the ring of Witt vectors over the algebraic closure of $\mathbb{F}_p$

2. Algebraic closure of the field of p-adics (which is the field of fractions of the ring of Witt vectors over $\mathbb{F}_p$)

In other words, does the operation of taking the field of fractions of the ring of Witt vectors commute with the operation of taking the algebraic closure?