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 $m,n \in \mathbb{N}$
27766
Comaximal ideals in a commutative ring
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.
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.
109199
Prove that every nonzero prime ideal is maximal in $\mathbb{Z}[\sqrt{d}]$
116883
About ideals in a ring which is a $k$ vector space
28244
Is the ideal $I = \{f\mid f (0) = 0\}$ in the ring $C [0, 1]$ of all continuous real valued functions on $[0, 1]$ a maximal ideal?
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
17239
Find all ideals of ${\mathbb{Z}_n}$
43889
Prove that $u-i$ is a maximal ideal of $\frac {\Bbb C[X,Y]} {\left (X^2+Y^2-1 \right )}.$
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 $R$.
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
49875
Question on Comaximal Ideals
43774
Given distinct maximal ideals $M_1,...,M_n$, is $M_1\cdots M_n$ radical?
49521
In an extension of finitely generated $k$-algebras the contraction of a maximal ideal is also maximal
72640
$(m,n) = (\gcd(m,n))$ as ideals in $\Bbb Z$
33245
Show that every ideal of the ring $\mathbb Z$ is principal
104782
Polynomial irreducible - maximal ideal