Assume r is commutative ring. prove that the following are, Ask an Expert

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Assume R is commutative ring. Prove that the following are equivalent:

a) R has exactly 1 prime ideal

b) Every element of R is either nilpotent or a unit.

c) R/N(R) is a field

Here N(R) denotes the nilradical of R. The set of nilpotent elements form an ideal called the nilradical of R

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