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Prove or disprove (a) Z[x]/(x^2 + 1), (b) Z[x]/(x^2 - 1) is an Integral domain. By...

Prove or disprove (a) Z[x]/(x^2 + 1), (b) Z[x]/(x^2 - 1) is an Integral domain.

By showing (a) x^2+1 is a prime ideal or showing x^2 + 1 is not prime ideal.

By showing (b) x^2-1 is a prime ideal or showing x^2 - 1 is not prime ideal.

(Hint: R/I is an integral domain if and only if I is a prime ideal.)

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