Question

(6) (a) Give an example of a ring with 9 elements which is not a field....

(6) (a) Give an example of a ring with 9 elements which is not a field. Explain your
answer.

(b) Give an example of a field of 25 elements. Explain why.

(c) Find a non-zero polynomial f(x) in Z3[x] such that f(a) = 0 for every a ? Z3.

(d) Find the smallest ideal of Q that contains 3/4.

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