Proving every prime ideal is maximal in a finite dimensional ring over a field.
7828
Proof that an integral domain that is a finite-dimensional $F$-vector space is in fact a field
111114
Prove that an ideal in $k[x,y]$ is a prime ideal
44083
prove that maximal ideal in $\mathbb{Z}$ generated by a prime number
40975
Quotient of the ring of integers of a number field by a prime ideal
5360
Ideal contained in a finite union of prime ideals
151829
Why are maximal ideals prime?
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
33245
Show that every ideal of the ring $\mathbb Z$ is principal
56800
Intersection of prime ideals
74537
Maximal Ideals in $K[y]$
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
76661
Checking the maximality of a principal ideal in $R[x]$
6699
An ideal that is maximal among non-finitely generated ideals is prime.
51578
Noetherian ring with finitely many height $n$ primes
21604
A complete ring with respect to an ideal
157585
Structure theorem of finite rings
67669
Prime ideals of a finite direct product ring