ON HOMOLOGICAL DIMENSIONS OF SIMPLE MODULES OVER NONCOMMUTATIVE RINGS

It is known that for a simple module S over a commutative ring R, fd(R )(S) = id(R)(S). Let R, T be commutative rings and R --> T a ring homo morphism, if T is a Noetherian ring and self-injective, then fd(R)(T) = id(R)(T). In this paper we use the equalities of mixed functors to g eneralize these results over non-commutative rings.