If $R$ is a ring and $M$ be any maximal ideal with $a\notin M$, then there exists $q\in M$ and $s\in R$ such that forall $r\in R$ $r=sar+qr$
136710
Prove that for every $a\in A$ $\exists$ $q\in M,s\in A$ s.t. $a=sba+qa$ where $M$ is maximal ideal in $A$.
128861
If $M$ isn't Noetherian, $M$ has a submodule maximal with respect to being not finitely generated.
111996
Maximal and Prime Ideal in Z
111189
Intersection of all maximal ideals containing a given ideal
6646
A (non-artificial) example of a ring without maximal ideals
81296
If A and B are ideals of a ring, show that A + B = $\{a+b|a \in A, b \in B\}$ is an ideal
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
104377
Maximal Ideals in Ring of Continuous Functions
74537
Maximal Ideals in $K[y]$
121750
Let $R$ be a commutative, unital ring and let $I$ be an ideal of $R.$ Prove that if $I$ is maximal then $R/I$ is a field.
139794
In a (not necessarily commutative) ring, a nilpotent maximal ideal is unique.
38228
Let $R$ be a Artinian commutative ring with $1 \neq 0$. If $I$ is prime, then $I$ is maximal.
42170
$R$ integral domain where every prime ideal is principal then set of non-principal ideals has maximal element
67237
Pull back image of maximal ideal under surjective ring homomorphism is maximal
6699
An ideal that is maximal among non-finitely generated ideals is prime.
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$