Only ideals of $M_n(\mathbb{F})$ are $M_n(\mathbb{F})$ and $\{0\}$
38817
Why is the ring of matrices over a field simple?
103518
If $J$ is the ideal generated by all idempotents in a prime ideal, then $R/J$ has only trivial idempotents
81982
Is $\mathbb{Z}[x]$ a principal ideal domain?
93723
Find all the maximal ideals in the ring $\mathbb{R}[x]$.
63207
Zorn's lemma and maximal ideals
47134
Ideals generated by two elements
102341
Primary decomposition of a monomial ideal
587
Ideal Generated by the Union of Two Ideals
138572
Is $(xy-1)$ a maximal ideal in $\mathbb C[x,y]$?
75614
Proving that $n|m\implies f_n|f_m$
29126
Maximal ideal in the ring of continuous functions from $\mathbb{R} \to \mathbb{R}$
144250
subideals of an ideal
21840
Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
41629
Structure of ideals in the product of two rings
90314
Maximal ideals in $R[x]$
3327
Height and minimal number of generators of an ideal
122012
The ideal $(x,y)$ is not a free $K[x,y]$-module