If $R$ is a commutative simple ring with identity , then is any matrix ring $M_n(R)$ also simple?
111786
for any ring $A$ the matrix ring $M_n(A)$ is simple if and only if $A$ is simple
82953
In a ring with no zero-divisors, for $(m,n) =1$, $a^m = b^m$ and $a^n = b^n$ $\iff a =b$
25430
When is matrix multiplication commutative?
142612
Matrix Ring of a Semisimple Ring
28688
why is a simple ring not semisimple?
122958
$R/I$ is commutative iff $rs-sr \in I$
10254
Is the Polynomial Factor Theorem true over all commutative rings?
118073
Is the ring $m\mathbb{Z}$ isomorphic to the ring $n\mathbb{Z}$?
82609
Ring such that $x^4=x$ for all $x$ is commutative
108012
A matrix $M$ that commutes with any matrix is of the form $M=\alpha I$
155445
What kind of ring $R$ makes $\mathcal O(\mathrm{Proj}\,R[x_0,\cdots,x_n])=R$?
16602
Proving $M_n(I)\lhd M_n(R)$ and proofs about ideal rings.
51593
Every finite commutative ring with no zero divisors contains a multiplicative identity?
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 $R$.
63338
Noncommutative failure of IBN: $\,R^n\cong R^m \Rightarrow n - m,$ ring $R$ with maximal ideal $I$ such that $R/I$ is not a division ring?
18971
Show that a ring is commutative if it has the property that ab = ca implies b = c when $a\neq 0$
102316
why $(r+I)(s+I) = rs + I$ in the quotient ring $R ?$