Let $R$ be a finite commutative ring with unity. Show that every prime ideal of $R$ is maximal.
53770
Let $R$ be a finite commutative ring. Show that an ideal is maximal if and only if it is prime.
138826
To show that either $R$ is a field or $R$ is a finite ring with prime number of elements and $ab = 0$ for all $a,b \in R$.
74537
Maximal Ideals in $K[y]$
85206
Verifying proof :an Ideal $P$ is prime Ideal if $R/P$ is an integral domain.
33245
Show that every ideal of the ring $\mathbb Z$ is principal
91180
Show $R \setminus S$ is a union of prime ideals
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal
68202
Must an ideal generated by an irreducible element be a maximal ideal?
90889
Prime ideals in a finite direct product of rings
70751
A commutative ring whose all proper ideals are prime is a field.
92585
If krull dimension is $0$, then all prime ideals are maximal?
30714
A question on ring homomorphisms and maximal ideals.
129371
Maximal ideals in the ring of real functions on $[0,1]$
67203
Complement of maximal multiplicative set is a prime ideal
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
118306
$I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]