If R is a finite commutative ring with unity, prove that every prime ideal of R is a maximal.

Proof. Suppose that <p> is a prime ideal of R, then p is a prime. Let p | ab, we have p|a or p|b. Let , I wish to show that J = R.

What can I use here?

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- Nov 26th 2007, 01:45 PMtttcomraderPrime ideal and maximal
If R is a finite commutative ring with unity, prove that every prime ideal of R is a maximal.

Proof. Suppose that <p> is a prime ideal of R, then p is a prime. Let p | ab, we have p|a or p|b. Let , I wish to show that J = R.

What can I use here? - Nov 26th 2007, 07:08 PMThePerfectHacker