collection of all non invertible elements in the ring is the maximal ideal
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
89313
Maximal ideals of polynomial rings in infinitely many variables
114640
Showing that an ideal is not a free $R-$module.
67237
Pull back image of maximal ideal under surjective ring homomorphism is maximal
139794
In a (not necessarily commutative) ring, a nilpotent maximal ideal is unique.
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
116430
If $I = \langle 2\rangle$, why is $I[x]$ not a maximal ideal of $\mathbb Z[x]$, even though $I$ is a maximal ideal of $\mathbb Z$?
57198
How to show that a valuation ring has a unique maximal ideal?
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
99567
Proving that an inverse ring homomorphism of an ideal is an ideal?
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
49303
In a noetherian integral domain every non invertible element is a product of irreducible elements
143051
Inverting noninvertible elements in a bigger ring.
121008
A non-noetherian ring with all localizations noetherian
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 $R$.
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.