On absolutely torsion-free rings

Let K(R) denote the set of the kernel functors of the ring R and let be the trivial kernel functor defined by setting oo() = M for every right module M. The absolutely torsion-free rings, that is, the rings R for which (R) = 0 for all G K(R), cr^oo, have been introduced by Rubin as a non commutative analogue of the integral domains.