Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
92071
A maximal ideal is always a prime ideal?
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
45684
Is quotient of a ring by a power of a maximal ideal local?
114329
Example of subring that is not an ideal
53367
In a principal ideal domain, prove that every non trivial prime ideal is a maximal ideal. What could be wrong in this approach?
80232
Suppose that R is a commutative ring with unity such that for each $a$ in $R$ there is an integer $n > 1\mid a^n =a$. Every prime ideal is maximal?
111679
Example of a ring without unity that has a subring with unity?
51593
Every finite commutative ring with no zero divisors contains a multiplicative identity?
110984
Ideals and prime ideals in a commutative ring.
54916
Maximal ideal in commutative ring
144572
Proof that ideals in $C[0,1]$ are of the form $M_c$ that should not involve Zorn's Lemma
27766
Comaximal ideals in a commutative ring
3037
Integral domain without unity has prime characteristic?
143884
A non-noetherian ring with noetherian spectrum
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
9792
Is there an example of a power of prime ideal in a polynomial ring that is not primary?