The radical of an ideal I in a ring R with identity is the intersection of all its minimal prime ideals [see Exercise 6].

Data from exercise 6

Let R have an identity. A prime ideal Pin R is called a minimal prime ideal of the ideal I if I ⊂ P and there is no prime ideal P' such that I ⊂ P'

(a) If an ideal I of R is contained in a prime ideal P of R, then P contains a minimal prime ideal of I. 

(b) Every proper ideal possesses at least one minimal prime ideal.

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CP.