Let R be a ring with no zero divisors such that for any [tex]r,s\in R[/tex], there exist [tex]a,b \in R[/tex] such that [tex]ar+bs=0[/tex]. Prove: [tex]R=K \oplus L[/tex] implies [tex]K=0[/tex] or [tex]L=0[/tex].
Definition of direct sum of modules, integral domain...
The Attempt at a Solution
I didn't know where to start on this one. In particular, I don't see what the hypothesis has to do with anything and certainly I do not see how it's related to the conclusion. I think all I need is a nudge in the right direction.