Mark each of the following true or false. 

____a. Every field is a UFD. 

____ b. Every field is a PID. 

____ c. Every PID is a UFD. 

____ d. Every UFD is a PID. 

____ e. Z[x] is a UFD. 

____ f. Any two irreducibles in any UFD are associates. 

____ g. If Dis a PID, then D[x] is a PID. 

____ h. If Dis a UFD, then D[x] is a UFD. 

____ i. In any UFD, if p|a for an irreducible p, then p itself appears in every factorization of a. 

____ j. A UFD has no divisors of 0.