Generalized Bousfield Lattices and a Generalized Retract Conjecture

Abstract

In [1], Bousfield studied a lattice (Bousfield lattice) on the stable homotopy category of spectra, and in [5], Hovey and Palmieri made the retract conjecture about that lattice. In this paper we generalize the Bousfield lattice and the retract conjecture to ones on a monoid. We also determine the structure of typical examples of generalized Bousfield lattices which satisfy the generalized retract conjecture. In particular we give explicitly the structure of the Bousfield lattice of the stable homotopy category of harmonic spectra.