If $M/N\cong M$, can we conclude that $N=0$?
75641
Is there a (f.g., free) module isomorphic to a quotient of itself?
14693
$d = \gcd(c,m),\ ac≡bc\pmod{\! m}\Rightarrow a≡b\pmod {\!m/d}\ $ [Congruence Cancellation & Division Rule]
140471
Is $ G \cong G/N \times N$?
133238
Why does $\mathrm{Tor}_0^R(M,N)\cong M\otimes_R N$?
18245
How to check if a system of congruence is solvable?
132672
Are $\log_1 1$ and $\log_0 0$ indeterminate forms?
40784
$\sum_{k=m}^{n}(-1)^k\binom{n}{k}\binom{k}{m}=0, n>m\geq 0$
81267
A simple doubt in number theory problem.
29204
$a\equiv\bar a\!\pmod{\!kn}\Rightarrow a\equiv\bar a\!\pmod{\! n};\ $ $(a\bmod kn)\bmod n=a\bmod n.\ $ Congruences persist mod factors of the modulus
106698
$\mathbb N$ when given the metric $d(m,n)=\frac{1}{m}-\frac{1}{n}$
8374
How to prove that $R/I \otimes_R M \cong M / IM$
148455
Show that if $(a,n)=d>1$ and $k$ is any positive integer, then $a^k\not\equiv 1\pmod{n}.$
32525
If $f(1)=1$, then is it true that $f(n)=n$ for all $n \in \mathbb{N}\cup\{0\}$.
106380
What is $n!$ when $n=0$?
5577
If $m$ divides $n$, find a free resolution of $\mathbb{Z}/m$ as a $\mathbb{Z}/n$-module.
70418
Theorem 3.2 Rudin -- How is 0 concluded?
135808
Show that there is a positive integer $n$ such that $G \cong \ker(\phi^{n}) \times \phi^{n}(G)$