Example of a finite commutative ring $R$ and an ideal $I$ where $I$ is maximal but not prime?
128813
Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
116943
Proof for maximal ideals in $\mathbb{Z}[x]$
93641
A maximal ideal among those avoiding a multiplicative set is prime
149747
Prove that if I is a prime ideal of R then I[x] is a prime ideal of R[x]
75558
Counter-example for prime ideals in a non commutative ring.
107454
Why D/I is finite if I is a non-zero ideal of the ring of integers of a number field?
157876
If every prime ideal is maximal, what can we say about the ring?
86816
Example of two prime ideals whose intersection of the squares not equal to the square of the intersection
90889
Prime ideals in a finite direct product of rings
131497
Maximal ideal not containing the set of powers of an element is prime
62917
Associated Prime Ideals in a Noetherian Ring; Exercise 6.4 in Matsumura
27766
Comaximal ideals in a commutative ring
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 $m,n \in \mathbb{N}$
54345
Prove if a non-trivial ring $R$ has a unique maximal left ideal $J$ , then $J$ is two-sided and is also the unique maximal right ideal in $R$.
6307
maximal ideal not containing some expression
92519
ideal behind Maximal ideals are Prime ideals
2995
A finite dimensional algebra over a field has only finitely many prime ideals and all of them are maximal