Solution Found!
Prove that is a maximal ideal in Z5[x, y].
Chapter 14, Problem 43SE(choose chapter or problem)
QUESTION:
Prove that \(\langle x, y \rangle\) is a maximal ideal in \(Z_5[x, y]\).
Questions & Answers
QUESTION:
Prove that \(\langle x, y \rangle\) is a maximal ideal in \(Z_5[x, y]\).
ANSWER:Step 1 of 6
Solution: 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 5 and if we assert that
then we must have is a maximal ideal of the ring
. So it suffice to prove that
Claim: is isomorphic to as a ring.
Proof of the Claim: We will propose to show that