 Solution

ID: past-exam-of-the-rings-and-modules-course-of-the-university-of-oxford/2017/1/b/i/solution

Take $R = Z /4 Z$ , a quotient ring with four residue classes. The class

\overline{2}

is nonzero but

\overline{2} \overline{2} = \overline{0}

. Thus

R

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