# Question: problem 3 let a be a ring and let i...

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Problem 3. Let A be a ring, and let I, P ⊂ A be ideals of A such that I ⊂ P.

Show that the following are equivalent:

(a) P is a prime ideal of A;

(b) P/I is a prime ideal of A/I.

Problem 3. Let A be a ring, and let I, P ⊂ A be ideals of A such that I ⊂ P.

Show that the following are equivalent:

(a) P is a prime ideal of A;

(b) P/I is a prime ideal of A/I.