Let $R=M_n(D)$, $D$ is a division ring. Prove that every $R-$simple module is isomorphic to each other.
33063
Are all simple left modules over a simple left artinian ring isomorphic?
137739
Prove that the group isomorphism $\mathbb{Z}^m \cong \mathbb{Z}^n$ implies that $m = n$
17978
Isomorphism classes of $\mathbb{Z}[i]$ modules.
85752
Show that $M=\frac{\mathbb{Z}^3}{\langle (3,3,1),(2,2,2)\rangle}$ is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}_4$ as $\mathbb{Z}$-modules
151803
Prove that $R$ is commutative
1686
Show that quotient rings are not isomorphic
8374
How to prove that $R/I \otimes_R M \cong M / IM$
8417
Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$
97608
Showing a Ring of endomorphisms is isomorphic to a Ring
141149
Proof some module is direct sum by its submodules.
38153
Looking for a simple proof that groups of order $2p$ are up to isomorphism $\mathbb{Z}_{2p}$ and $D_{p}$ .
154581
Ring of matrices isomorphic to $O := \left\{a+b\frac{1+\sqrt{D}}{2}: a, b \in \mathbb{Z} \right\}$
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
158232
Tensor product of a module with an ideal is isomorphic to their standard product
158583
Prove that if $M$ is an $R-$ projective left module then $M/IM$ is an $R/I-$ projective left module.
61491
Complex Ring Isomorphism
107163
Proof that $S_3$ isomorphic to $D_3$