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(a) Describe the unit groups of the rings Z and Z[I]. [7] (b) Are there zero divisors in the ring of integers? [3] (C)

(a) Describe the unit groups of the rings Z and Z[I]. [7] (b) Are there zero divisors in the ring of integers? [3] (C) Determine with reason if each of the following statements is true or false. () Every ideal is a subring for any ring R. [5] (ii) The kernel of a ring homomorphism f : R Sis an ideal of R. [5]

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