Prove that the ring $\mathbb{Z}_n$ contains a nonzero element $a$, such that $a^2=0$ if and only if $p^2|n$ for some prime p
12900
Nonzero nilpotent elements in Zn
1720
Show that $\langle 2,x \rangle$ is not a principal ideal in $\mathbb Z [x]$
115920
Showing $R$ is a local ring if and only if all elements of $R$ that are not units form an ideal
8494
Proof Check: Number of elements of $\mathbb{F}_{p^{n}}$ of the form $a^{p}-a$ for some $a \in \mathbb{F}_{p^{n}}$.
51593
Every finite commutative ring with no zero divisors contains a multiplicative identity?
64782
How to prove if $n$ is prime and $n | a^2$ then $n | a$?
115782
Proof $\mathbb{A}^n$ is irreducible, without Nullstellensatz
28136
$A^m\hookrightarrow A^n$ implies $m\leq n$ for a ring $A\neq 0$
40975
Quotient of the ring of integers of a number field by a prime ideal
116000
Prove that prime ideals of a finite ring are maximal
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
7303
How many idempotent elements does the ring ${\bf Z}_n$ contain?
96071
How to show that a prime ideal of height 2 can’t necessarily be generated by 2 elements? (Hartshorne exercise I.1.11)
154305
Let $\pi$ denote a prime element in $\mathbb Z[i], \pi \notin \mathbb Z, i \mathbb Z$. Prove that $N(\pi)=2$ or $N(\pi)=p$, $p \equiv 1 \pmod 4$
43990
R is a commutative ring with $1\ne 0$ and $R^m \cong R^n$, then $m=n$
31585
Primary ideals of $\mathbb{Z}$
157863
A finite pseudo-ring such that $ab^2=b$ for some $(a,b)\in A$