Over non-commutative ring, Free modules of different ranks might be isomorphic?
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?
77198
Showing that the characteristic of a commutative ring R without zero divisors is 0 or prime
12474
Does an injective endomorphism of a finitely-generated free R-module have nonzero determinant?
40996
Proving that free modules are flat (without appealing projective modules)
128813
Examples of a commutative ring without an identity in which a maximal ideal is not a prime ideal
47630
Endomorphisms of modules satisfying chain conditions and counterexamples.
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?
28327
(Simple) Examples on Non-Commutative Rings
120035
Pattern in Isomorphisms between $\mathbb Z_m \times \mathbb Z_n$ and $\mathbb Z_{mn}$
78053
There are at least three mutually non-isomorphic rings with $4$ elements?
6385
Minimal counterexamples of the isomorphism problem for integral group rings
118911
Classifying Unital Commutative Rings of Order $p^2$
66169
Ring of order $n$ is isomorphic to $\Bbb Z/n\Bbb Z$, with $n$ square-free
144442
Let $R$ be a commutative unital ring. Is it true that the group of units of $R$ is not isomorphic with the additive group of $R$?
75641
Is there a (f.g., free) module isomorphic to a quotient of itself?
95942
$k[x]/(x^n)$ module with finite free resolution is free
123130
Showing an isomorphism between exterior products of a free module