Does maximal ideal exist in a commutative ring without identity?
6646
A (non-artificial) example of a ring without maximal ideals
129371
Maximal ideals in the ring of real functions on $[0,1]$
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 $R$.
118306
$I:=\{f(x)\in R\mid f(1)=0\}$ is a maximal ideal?
6307
maximal ideal not containing some expression
29019
Ideals in direct product of rings
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
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.
18406
An ideal whose radical is maximal is primary
27766
Comaximal ideals in a commutative ring
137450
Two-sided ideal generated by subset of not commutative ring
111996
Maximal and Prime Ideal in Z
87780
Is the ideal $(2,X+1)\subset\Bbb{Z}[X]$ prime, maximal or neither?
94532
How to prove a commutative, with unit, Noetherian ring $A$ only has finitely many minimal prime ideals via the following step?
3129
A commutative ring is a field iff the only ideals are $(0)$ and $(1)$
104486
Ideal in $\mathbb Z[x]$ which is not two-generated
76661
Checking the maximality of a principal ideal in $R[x]$