# Explore Our Questions

9
5
404
views

1
vote
1
34
views

3
2
72
views

### $r$ is not nilpotent, $r-r^2$ is nilpotent, then the ring has a non-zero idempotent

1h ago YACP 15.3k
6
4
64
views

### How do you prove that $\Bbb{Z}_p$ is an integral domain?

2h ago anon 50.8k
3
1
179
views

### Maximal ideal of ring of matrices

5h ago Babgen 1,453
5
3
44
views

1
vote
1
52
views

2
1
35
views

### Understanding an example of the product of two finite cyclic groups in MacLane/Birkhoff's Algebra

6h ago anon 50.8k
4
1
3
kviews

### How to write permutations as product of disjoint cycles and transpositions

7h ago YACP 15.3k
2
3
197
views

### Prove that $\mathbb Z_{m}\times\mathbb Z_{n} \cong \mathbb Z_{mn}$ implies $\gcd(m,n)=1$.

7h ago YACP 15.3k
1
vote
2
32
views

### Finite extensions of nilpotent groups

7h ago YACP 15.3k
1
vote
0
62
views
+50

8h ago user 933
2
2
76
views

### Show that the mapping $x\rightarrow x^{-1}$ of $G$ onto $G$ is an isomorphism iff $G$ is abelian

9h ago amWhy 107k
4