example of noncommutative rings $A$ such that $A^2 \cong A$ as left $A$-modules
46843
A ring without the Invariant Basis Number property
76100
Showing that $\left\langle a,b \mid abab^{-1}\right\rangle \cong \pi_1(K) \cong \left\langle c,d \mid c^2 d^2 \right\rangle$
127030
Simple example of non-arithmetic ring (non-distributive ideal lattice)
128813
Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?
105363
$\mathbb Z^n/\langle (a,...,a) \rangle \cong \mathbb Z^{n-1} \oplus \mathbb Z/\langle a \rangle$
138337
On a ring $R$ where $x^2 = x$, we must have that $2x = 0$ and $R$ is commutative
42774
Examples of involutions on $\mathbb{R}$
80302
A module $M$ whose submodules and factor modules are semisimple but not semisimple itself
102072
Simple $M_n(D)$-module with $D$ a division ring
131671
Let R be a ring such that $a^2 = a$ , $\forall a$ $\in R$ . Prove that R is commutative.
135781
Division ring if and only if it has no proper left ideals.
76749
Example of a finite non-commutative ring without a unity
7870
For $M\otimes_R N$, why is it so imperative that $M$ be a right $R$-module and $N$ a left $R$-module?
133878
Ring of order $p^2$ is commutative.
118911
Classifying Unital Commutative Rings of Order $p^2$
8417
Natural $(R/I)$-module structure for an $R$-module $M$ annihilated by $I$