Mark each of the following true or false. ___ a. Let F() be any simple extension of

Mark each of the following true or false.
___ a. Let F(α) be any simple extension of a field F. Then every isomorphism of F onto a subfield of F̅ has an extension to an isomorphism of F(α) onto a subfield of F̅.
___ b. Let F(α) be any simple algebraic extension of a field F. Then every isomorphism of F onto a subfield of F has an extension to an isomorphism of F(α) onto a subfield of F̅.
___ c. An isomorphism of F onto a subfield of F̅ has the same number of extensions to each simple algebraic extension of F.
___ d. Algebraic closures of isomorphic fields are always isomorphic.
___ e. Algebraic closures of fields that are not isomorphic are never isomorphic.
___ f. Any algebraic closure of Q(√2) is isomorphic to any algebraic closure of Q(√17).
___ g. The index of a finite extension E over a field F is finite.
___ h. The index behaves multiplicatively with respect to finite towers of finite extensions of fields.
___ i. Our remarks prior to the first statement of Theorem 49.3 essentially constitute a proof of this
theorem for a finite extension E over F.
___ j. Corollary 49.5 shows that C is isomorphic to Q̅.