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

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- Mar 14th 2013, 12:27 AMojasring theory
show that a unit of a ring divides every other element of the ring

- Mar 14th 2013, 12:53 AMGusbobRe: ring theory
$\displaystyle a$ is unit in a ring $\displaystyle R$, so there is an element $\displaystyle a^{-1}$ such that $\displaystyle aa^{-1}=1$. By associativity, $\displaystyle b=a(a^{-1}b)$ for any element $\displaystyle b\in R$.

- Mar 14th 2013, 08:33 AMHartlwRe: ring theory