An. Krasilnikov et Sm. Vovsi, ON FULLY INVARIANT IDEALS OF THE FREE GROUP-ALGEBRA, Proceedings of the American Mathematical Society, 124(9), 1996, pp. 2613-2618
Let RF be the group algebra of a free noncyclic group F over an integr
al domain R. It is proved that if R is not a field, then there exists
a fully invariant ideal I of RF such RF/I is torsion-free but not proj
ective as an R-module. In other words, there exists a pure nonprojecti
ve variety of group representations over R.