Brittney Lord

2020-11-22

Suppose that R and S are commutative rings with unites, Let

a. If A is prime in S, show that

b. If A is maximal in S, show that

stuth1

Skilled2020-11-23Added 97 answers

a. Suppose A i sprime ideal in S.

Consider

Since A is prime, either

Hence either a or b belongs to

Thus,

b. Consider the homomorphism phi:

Then the kernel of

Then,

Therefore,

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