See Question.pdf

**Subject Mathematics Abstract Algebra**

See Question.pdf

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Let S and T be subfields of F.

We first show that the intersection of S and T is non-empty. Let 0 denote the identity element with respect to addition in F. Since S and T are both subfields of F, each must contain 0, and therefore 0 is in the intersection.

We next show that the intersection is a commutative ring.

First the intersection is closed under addition + and multiplication...

We first show that the intersection of S and T is non-empty. Let 0 denote the identity element with respect to addition in F. Since S and T are both subfields of F, each must contain 0, and therefore 0 is in the intersection.

We next show that the intersection is a commutative ring.

First the intersection is closed under addition + and multiplication...

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