# ring theory

• March 14th 2013, 12:27 AM
ojas
ring theory
show that a unit of a ring divides every other element of the ring
• March 14th 2013, 12:53 AM
Gusbob
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 $b\in R$.
• March 14th 2013, 08:33 AM
Hartlw
Re: ring theory
Quote:

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