If R is a local ring, then its maximal left-ideal is a left and right ideal
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 $R$.
587
Ideal Generated by the Union of Two Ideals
135781
Division ring if and only if it has no proper left ideals.
136654
$(x_1-a_1, x_2-a_2)$ is a maximal ideal of $K[x_1,x_2]$
89313
Maximal ideals of polynomial rings in infinitely many variables
158583
Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
111189
Intersection of all maximal ideals containing a given ideal
133975
Localising a polynomial ring and non-maximal prime ideal
18406
An ideal whose radical is maximal is primary
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.
149412
Every prime ideal of a finitely generated $\mathbb{R}$-algebra is an intersection of maximal ideals?
73417
$Rad(I)$ is an ideal of $R$
43230
Is $\langle1-i\rangle$ a maximal ideal in $\mathbb{Z}[i]$?
92071
A maximal ideal is always a prime ideal?
104782
Polynomial irreducible - maximal ideal
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
138572
Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?