Mark each of the following true or false. 

___ a. If a field E is a finite extension of a field F, then E is a finite field. 

___ b. Every finite extension of a field is an algebraic extension. 

___ c. Every algebraic extension of a field is a finite extension. 

___ d. The top field of a finite tower of finite extensions of fields is a finite extension of the bottom field. 

___ e. Q is its own algebraic closure in R, that is Q is algebraically closed in R 

___ f. C is algebraically closed in C(x), where x is an indeterminate. 

___ g. C(x) is algebraically closed, where x is an indeterminate. 

___ h. The field C(x) has no algebraic closure, since re already contains all algebraic numbers. 

___ i. An algebraically closed field must be of characteristic 0.

 ___ j. If E is an algebraically closed extension field of F, then E is an algebraic extension of F.