on injectivity of certain gorenstein injective modules

In this note, we will be concerned with injectivity of gorensteininjective modules over certain rings. specically, we will show that if r is acomplete local d-gorenstein ring and m is a gorenstein injective r-modulepossessing a syzygy kn, n  d such that ?kn k?n = add (kn) [ inj(r),then m is injective. this is particularly related to the dual notion of thefamous auslaner-reiten conjecture recently posed.