Group rings that are exact

A ring R   is left exact if, for every finitely generated left submodule S⊂RnS⊂Rn, every left R-linear function from S to R extends to a left R  -linear function from RnRn to R. The class of exact rings generalizes that of self-injective rings and has been introduced in a recent paper by Wilding, Johnson, and Kambites. In our paper we show that the group ring of a group G over a ring R is left exact if and only if R is left exact and G is locally finite.