Let R be a ring with no zero divisors such that for all r,s R there

Let R be a ring with no zero divisors such that for all r,s ϵ R there exist a, b ϵ R, not both zero, with ar + bs = 0.

(a) If R = K⊕L (module direct sum), then K = 0 or L = 0.

(b) If R has an identity, then R has the invariant dimension property.