Question

1. a) Let C and H be groups of orders p, q where p and q are distinct primes. Show that any homomorphism from G to H must take any element of G to the identity element of H.

b) Show that if R.is a commutative ring with no zero divisors, then the polynomial ring R[X] has no zero divisors.

c) Find the quotient field of z[ root under 3 ] = {a + b(root under 3) la, b belongs to z}.

.