Let $R$ be a ring and let $a \in R$. Let $n \in N$. Show that if $a^n$ has an inverse, a has an inverse.
109470
Proof of whether a specific element is in a commutative, invertible monoid.
74559
$A$ and $B$ are ideals of a ring ${R}$ such that $A\cap B=\{0\}$. Prove that $st=0$ for every $s\in A, t\in B$.
107900
A ring which has many distinct left inverses
96152
Showing that $a^n - 1 \mid a^m - 1 \iff n \mid m$
33344
A different way to show that $a^k-1 \mid a^n-1$ if $k\mid n$?
110464
Let $A=\{1,...,n\}.$ Show that there is a bijection of $P(A)$ with the cartesian product $X^n$ where $X$ is the two element set $X=\{0,1\}$
1315
Let $R$ be a ring. Define a circle composition ◦ in R by $a ◦ b =a+b-ab$, $a, b ∈ R$.
11573
Rings and some of their properties
152223
If $0<r<1$ show that $r^n$ goes to $0$ as $n$ goes to 1.
14403
If $n = p_1^{a_1} ... p_r^{a_r}$ the set of nilpotents of $\mathbb{Z}_n$ is $(p_1 p_2 ... p_{r-1} p_r)\Bbb Z_n$
107378
If a ring element is right-invertible, but not left-invertible, then it has infinitely many right-inverses.
83255
Finding inverse in non-commutative ring
22666
Proving that if $A^n = 0$, then $I - A$ is invertible and $(I - A)^{-1} = I + A + \cdots + A^{n-1}$
150309
Why do we assume $a+b=b+a$ in a Ring with 1. Also, is it true with Rings without 1?
50908
Showing a Ring and an Ideal are equal
127418
If ring $B$ is integral over $A$, then an element of $A$ which is a unit in $B$ is also a unit in $A$.
85913
R is commutative ring with identity & define $\circ$ on $R$ by for any $a,b \in R$ $a \circ b=a+b-ab$ Prove the following