$R$ is simple iff $M_n(R)$ is simple for rings without identity
111786
for any ring $A$ the matrix ring $M_n(A)$ is simple if and only if $A$ is simple
19112
Ring $R= \mathbb Z_3[x]/\langle x^6-1\rangle$
112577
$\hom (M, \coprod_i N_i) \cong \bigoplus_i \hom (M, N_i)$ in abelian categories when $M$ is simple?
126644
Simple module and homomorphisms
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
79957
If $R$ is an infinite ring, then $R$ has either infinitely many zero divisors, or no zero divisors
38549
$\mathbb{Q}(\sqrt{n}) \cong \mathbb{Q}(\sqrt{m})$ iff $n=m$
121465
$R[x]$ has a subring isomorphic to $R$.
102072
Simple $M_n(D)$-module with $D$ a division ring
69353
Show that a ring with only trivial right ideals is either a division ring or $|R|=p$ and $R^2=\{0\}$. Why would $R$ be finite?
9846
Prove $n-m \mid n^r - m^r\,$ [Factor Theorem, monomial case]
8374
How to prove that $R/I \otimes_R M \cong M / IM$
152013
elementary ring proof with composition of functions and addition of functions as operations
70576
Elementary proof that $\mathbb{R}^n$ is not homeomorphic to $\mathbb{R}^m$
31729
Tensor products of simple modules over algebras
11573
Rings and some of their properties
23879
If $m$ and $n$ are distinct positive integers, then $m\mathbb{Z}$ is not ring-isomorphic to $n\mathbb{Z}$