manuscripta math. 84, 193 - 198 (1994) manuscripta mathematica (~ Springer-Verlag 1994 A REMARK ON THE GENERALIZED SMASHING CONJECTURE Bernhard Keller Using one of Wodzicki's examples of H-unital algebras [14] we exhibit a ring whose derived category contains a smashing subcategory which is not generated by small objects. This disproves the generalization to arbitrary triangulated categories of a conjecture due to Ravenel [8, 1.33] and, originally, Bousfield [2, 3.4]. 1. Statement of the conjecture We refer to [7] for a nicely written analysis of the following setup: Let S be a triangulated category [13] admitting arbitrary (set-indexed) coproducts. An object X 6 S is small if the functor Hom (X, ?) commutes with arbitrary coproducts. We denote the full subcategory on the small objects of S by S b. We suppose that Sb is equivalent to a small category. A full subcategory of S is localizing if it is a triangulated subcategory in the sense of Verdier which is closed under forming coproducts with respect to S. We suppose that 8 is generated by S b, i.e. coincides with its smallest localizing subcategory containing Sb.