Mark each of the following true or false. 

___ a. Z[i] is a PID. 

___ b. Z[i] is a Euclidean domain. 

___ c. Every integer in Z is a Gaussian integer. 

___ d. Every complex number is a Gaussian integer. 

___ e. A Euclidean algorithm holds in Z[i]. 

___ f. A multiplicative norm on an integral domain is sometimes an aid in finding irreducibles of the domain.

___ g. If N is a multiplicative norm on an integral domain D, then |N(u)| = 1 for every unit u of D.

___ h. If F is a field, then the function N defined by N(f(x)) = (degree of f(x)) is a multiplicative norm on F[x]. 

___ i. If F is a field, then the function defined by N(f (x)) = 2^{(Degree of f(x))} for f(x) ≠ 0 and N(0) = 0 is a multiplicative norm on F[x] according to our definition. 

___j. Z[√-5] is an integral domain but not a UFD.