Prove $Z_{mn}$ has at least $2$ idempotent elements besides $0$ and $1$.
102112
Idempotents in $\mathbb Z_n$
5226
Prove that a finite semigroup G with identity is a group if and only if G contains only one idempotent
147611
Given $P$ idempotent, show that $I-P$ is idempotent.
117688
Prove that $\def\Aut{\operatorname{Aut}}\Aut(\mathbf{Z_{n}})\simeq \mathbf{Z_{n}^{*}}$
104855
Prove that $N \subset Z(G)$
67926
$S_n$ is generated by elements of the form $(1k)$
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
118452
how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
59566
Proving that $ka \equiv kb \pmod{m} \iff a \equiv b \pmod{m/\gcd(k,m)}$
47709
If $n\mid m$ prove that the canonical surjection $\pi: \mathbb Z_m \rightarrow \mathbb Z_n$ is also surjective on units
69352
Prove that $I= \{a+bi \in ℤ[i] : a≡b \pmod{2}\}$ is an maximal ideal of $ℤ[i]$.
60674
Finitely generated idempotent ideals are principal: proof without using Nakayama's lemma
119052
Finding invertible elements in $\mathbb{Z}/m\mathbb{Z}$
158343
how to prove an element is non-zero in a tensor-product
52354
Given a idempotent endomorphism, show that $M = \ker(f) \oplus \ker (f-\text{id}_M)$
66134
Sufficiently many idempotents and commutativity