 Solution

ID: past-exam-of-the-algebra-analysis-and-differential-equations-1-course-of-the-university-of-oxford/2004/algebra/3/iv/solution

Z [i]

. It contains zero and one and is closed under addition, additive inverses and multiplication, since

(a + bi) (c + d i) = (a c - b d) + (a d + b c) i .

Its operations inherit the ring axioms from

C

. It is a ring but not a field: the nonzero element 2 has complex inverse

1/2

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