# Math Help - ring theory

1. ## ring theory

show that a unit of a ring divides every other element of the ring

2. ## Re: ring theory

$a$ is unit in a ring $R$, so there is an element $a^{-1}$ such that $aa^{-1}=1$. By associativity, $b=a(a^{-1}b)$ for any element $b\in R$.

3. ## Re: ring theory

Originally Posted by ojas
show that a unit of a ring divides every other element of the ring
1Ib if b=qx1 for some q.
q=b