Solution Found!
Prove that is a maximal ideal in Z[x, y].
Chapter 14, Problem 44SE(choose chapter or problem)
QUESTION:
Prove that \(\langle 2, x, y\rangle\) is a maximal ideal in Z[x, y].
Questions & Answers
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