An example of nonzero ring $R$ with $R^m\cong R^n$, $m\neq n$
133495
Example of a ring without Invariant Basis Property
74974
When $\operatorname{Hom}_{R}(M,N)$ is finitely generated as $\mathbb Z$-module or $R$-module?
21840
Zero divisors and units for the ring $\mathbb{Z}/n\mathbb{Z}$ with integer $n$
59902
Example of $2$ non-isomorphic groups that have the same quotients
9074
Example of non-isomorphic structures which are elementarily equivalent
102072
Simple $M_n(D)$-module with $D$ a division ring
142863
Show that every ideal of the matrix ring $M_n(R)$ is of the form $M_n(I)$ where $I$ is an ideal of $R$
127030
Simple example of non-arithmetic ring (non-distributive ideal lattice)
63568
Ring with finitely many zerodivisors
11541
Examples of a non-commutative division ring
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$
1686
Show that quotient rings are not isomorphic
35777
$\mathbb{R}[X,Y]/(Y-X^2,Y+X)\cong_\text{Ring} \mathbb{R}\times \mathbb{R}$
49166
$R^n \cong R^m$ iff $n=m$
76749
Example of a finite non-commutative ring without a unity
39049
Ring With Unity As a Direct Sum of Non-Zero Ideals
114329
Example of subring that is not an ideal