Self-orthogonal modules over coherent rings

Let R be a left coherent ring, S any ring and (R)omega (S) an (R,S)-bimodul e. Suppose omega (S) has an ultimately closed FP-injective resolution and ( R)omega (S) satisfies the conditions: (11) ws is finitely presented; (2) Th e natural map R --> End(omega (S)) is an isomorphism; (3) Ext(R)(l)(omega,o mega)= 0 for any i greater than or equal to 1. Then a finitely presented le ft R-module A satisfying Ext(R)(l)(A, omega)= 0 for any i greater than or e qual to 1 implies that A is omega -reflexive. Let R be a left coherent ring , S a right coherent ring and (R)omega (S) a faithfully balanced self-ortho gonal bimodule and n greater than or equal to 0. Then the FP-injective dime nsion of (R)omega (S) is equal to or less than n as both left R-module and right S-module if and only if every finitely presented left R-module and ev ery finitely presented right S-module have finite generalized Gorenstein di mension at most n. (C) 2001 Elsevier Science B.V. All rights reserved.