Proof: $\mathbb{Z}_n$ has zero divisors if and only if $n$ is not prime.
118452
how to prove $\mathbb Z_n$ has divisors of zero if and only if $n$ is not prime
77240
Show that $4 + \sqrt{10}$ is not prime in $\mathbb{Z}\bigl [\sqrt{10}\bigr]$
144622
Proof: If no prime less than or equal to $\sqrt{n}$ divides $n$, then $n$ is a prime
150007
Prove that $(\mathbb{Z}_n , +)$, the integers $\pmod{n}$ under addition, is a group.
78852
If $\gcd(m,n) =1, $ then $m\mathbb{Z}/ mn\mathbb{Z} \cong \mathbb{Z}/(n)$
33052
How to prove $\bar{m}$ is a zero divisor in $\mathbb{Z}_n$ if and only if $m,n$ are not coprime
19838
Prove that in general the set of the right zero divisors is different from the set of left zero divisors in a ring R
137858
Showing that $\mathbb{Z}[i]/I$ is a finite field whenever $I$ is a prime ideal, and also finding its cardinality?
66238
Proving $\mathbb{Z}[\sqrt {10}]$ is not a UFD
14055
How to show that a finite commutative ring without zero divisors is a field?
70463
Let $p$ be prime and $a$ be a natural not divisible by $p$. Then, $\exists$ integers $x,y$ such that $ax\equiv y \pmod{p}$ with $0<|x|,|y|<\sqrt{p}$
51952
Show that $x^{n-1}+\cdots +x+1$ is irreducible over $\mathbb Z$ if and only if $n$ is a prime.
69582
Is it true that: $a+bi$ is prime in $\mathbb{Z}[i]$ if and only if $a^2+b^2$ is prime in $\mathbb{Z}$
120407
Is every noninvertible matrix a zero divisor?
74441
Zero divisors in matrix rings
95764
Prove that the additive groups $\mathbb{Z}$ and $\mathbb{Q}$ are not isomorphic.
59533
If $\gcd(m,n)=1$, then $\mathbb{Z}_n \times \mathbb{Z}_m$ is cyclic.