Mark each of the following true or false. 

___ a. Every prime ideal of every commutative ring with unity is a maximal ideal. 

___ b. Every maximal ideal of every commutative ring with unity is a prime ideal. 

___ c. Q is its own prime subfield. 

___ d. The prime subfield of C is R 

___ e. Every field contains a subfield isomorphic to a prime field. 

___ f. A ring with zero divisors may contain one of the prime fields as a subring. 

___ g. Every field of characteristic zero contains a subfield isomorphic to Q. 

___ h. Let F be a field. Since F[x] has no divisors of 0, every ideal of F[x] is a prime ideal. 

___ i. Let F be a field. Every ideal of F[x] is a principal ideal. 

___ j. Let F be a field. Every principal ideal of F[x] is a maximal ideal.