Mark each of the following true or false. 

___ a. The concept of a ring homomorphism is closely connected with the idea of a factor ring. 

___ b. A ring homomorphism ∅ : R → R' carries ideals of R into ideals of R'. 

___ c. A ring homomorphism is one to one if and only if the kernel is {0}. 

___ d. Q is an ideal in R.

___ e. Every ideal in a ring is a subring of the ring. 

___ f. Every subring of every ring is an ideal of the ring. 

___ g. Every quotient ring of every commutative ring is again a commutative ring. 

___ h. The rings Z/4Z and Z₄ are isomorphic. 

___ i. An ideal N in a ring R with unity 1 is all of R if and only if 1 ∈ N. 

___ j. The concept of an ideal is to the concept of a ring as the concept of a normal subgroup is to the concept of a group.