Question: Exercise 1.9. Let R be a ring, and let N = nilrad( R) be the nilradical of R. Show that the following are equivalent. (1)

Exercise 1.9. Let R be a ring, and let N = nilrad( R) be the nilradical of R. Show that the following are equivalent. (1) R has exactly one prime ideal. (2) Every element of R is either a unit or nilpotent. (3) R/N is a field

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