Can an $R$-module have bases of different cardinality?
52088
Isomorphism of an endomorphism ring, how can $R\cong R^2$?
96845
Question: Compare the cardinality between the sets $\Bbb R$ and $\Bbb N^{\Bbb N}$
33207
Bases having countable subfamilies which are bases in second countable space
95747
Number of countable subsets of $\mathbb{R}$
14259
If M+N and M$\cap$N are finitely generated modules, so are M and N.
102112
Idempotents in $\mathbb Z_n$
150986
For a Noetherian ring $R$, we have $\text{Ass}_R(S^{-1}M)=\text{Ass}_R(M)\cap \{P:P\cap S=\emptyset\}$
114640
Showing that an ideal is not a free $R-$module.
134294
A (not necessarily unitary) $R$ module $M$ splits into $B\oplus C$ where $B$ is unitary and $RC=\{0\}$.
47015
Vector Space Structures over ($\mathbb{R}$,+)
74445
Noetherian and Artinian modules
36987
A criterion of flat modules
37570
$M + N$ and $M \cap N$ are finitely generated $A$-modules implies $M$ and $N$ finitely generated using exact sequences
145722
Prove there is a bijection between the set of $R[x]$-module structures on $M$ and $\mathrm{End}_{R-\mathsf{Mod}}(M)$.
66866
Algebraic dual of $\mathbb{R}^{\mathbb{N}}$
1117
Is there a bijection between $(0,1)$ and $\mathbb{R}$ that preserves rationality?
127233
Cardinality of order types in $\mathbb{N}$