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Let R be a ring, and let N be an ideal of R. Let γ :...

Let R be a ring, and let N be an ideal of R.
Let γ : R → R/N be the canonical homomorphism.
(a) Let I be an ideal of R such that I ⊇ N.
Prove that γ−1[γ[I]] = I.
(b) Prove that mapping
{ideals I of R such that I ⊇ N} −→ {ideals of R/N} is a well-defined bijection between two sets
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