Quotienting $\mathbb Z[x]$ by a maximal ideal gives a finite field.
29635
Fields finitely generated as $\mathbb Z$-algebras are finite?
52602
$K[X^2,X^3]\subset K[X]$ is a Noetherian domain and all its prime ideals are maximal
31585
Primary ideals of $\mathbb{Z}$
89313
Maximal ideals of polynomial rings in infinitely many variables
111996
Maximal and Prime Ideal in Z
131497
Maximal ideal not containing the set of powers of an element is prime
80879
Can a quotient field ever be finitely generated as an algebra?
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
75970
$\mathbb Z[1/2]$ is not finitely generated?
63207
Zorn's lemma and maximal ideals
87103
Quick question about ideals of field $F$ in $F[x]$ are principal.
93474
A Finite Boolean Ring is Generated by Finitely Many Copies of $\mathbb{Z} / 2 \mathbb{Z}$
16643
A slick proof that a field which is finitely generated as a ring is finite
68202
Must an ideal generated by an irreducible element be a maximal ideal?
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.
117005
Rules in the ring with coefficients in finite field $\mathbb{F}_p$
29626
Is there a proper subfield $K\subset \mathbb R$ such that $[\mathbb R:K]$ is finite?