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Prove that is a maximal ideal in Z[x, y].

Chapter 14, Problem 44SE

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QUESTION:

Prove that \(\langle 2, x, y\rangle\) is a maximal ideal in Z[x, y].

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QUESTION:

Prove that \(\langle 2, x, y\rangle\) is a maximal ideal in Z[x, y].

ANSWER:

Step 1 of 5

Let us consider the ring . We will propose to prove that the ideal  is a maximal ideal of the ring . Recall that,  is field of char 2 and if we assert that

then we must have  is a maximal ideal of the ring . So it suffice to prove that

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