To show that $\langle x-a , y-b\rangle$ is a maximal ideal of $F[x,y]$ by showing that $F[x,y]/\langle x-a , y-b\rangle$ is a field
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
50445
Explaining the product of two ideals
41069
Justifying $\,\Bbb{Z}[i]/\langle 2\rangle\cong \Bbb{Z}[X]/\langle X^2+1,2\rangle\cong \Bbb{F}_2[X]/\langle X^2+1\rangle$
63207
Zorn's lemma and maximal ideals
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
93658
Proving that an ideal in a PID is maximal if and only if it is generated by an irreducible
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
46040
Preimage of maximal ideal is maximal (why is this answer wrong?)
89313
Maximal ideals of polynomial rings in infinitely many variables
114343
If $I$ and $J$ are ideals in a ring $R$ with $1$ such that $I+J = R$, show that $I^m$ and $J^n$ are co-maximal for all $m,n \in \mathbb{N}$
97605
Let $f$ be a surjective homomorphism. Prove that $\ker(f)$ is a maximal ideal
587
Ideal Generated by the Union of Two Ideals
112150
Prove that the ideal $(x^2 + x+2)$ is maximal in $F_3[x]$
89271
If $F$ is a field, then $F[x]$ is a principal ideal domain proof question
111248
The Uniqueness of a Coset of $R[x]/\langle f\rangle$ where $f$ is a Polynomial of Degree $d$ in $R[x]$
18186
Prove that ideal $I = \langle X^2,X+1\rangle$ is principal or not (in $\mathbb{Z}[X]$ and $\mathbb{Q}[X]$ )
85752
Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules