Definition:Divisible Module

Definition

Let $R$ be a ring.

Let $M$ be a left $R$-module.

Let $M$ be such that:

for all $m \in M$

for all non zero divisors $r \in R$

there exists some $m' \in M$ such that $r m' = m$.

Then $M$ is (a) divisible (module).

Sources

• Barile, Margherita. "Divisible Module." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/DivisibleModule.html