Wakamatsu tilting modules with finite FP-injective dimension

摘要

Let R be a left coherent ring, Rω a Wakamatsu tilting module and S = End(Rω) a right coherent ring. It is shown that the FP-injective dimensions of Rω and ωs are identical provided both of them are finite. It is also shown that in this case all finitely presented left R-modules (right S-modules) have special ~-ω-precovers and special (~-ω)~--preenvelopes.