In algebraic topology, the Bousfield class of, say, a spectrum X is the set of all (say) spectra Y whose smash product with X is zero: X ⊗ Y = 0 {\displaystyle X\otimes Y=0} . Two objects are Bousfield equivalent if their Bousfield classes are the same. The notion applies to module spectra and in that case one usually qualifies a ring spectrum over which the smash product is taken.
See also Bousfield localization
External links Ncatlab.org
References Iyengar, Srikanth B.; Krause, Henning (2013-04-01). "The Bousfield lattice of a triangulated category and stratification". Mathematische Zeitschrift. 273 (3): 1215–1241. arXiv:1105.1799. doi:10.1007/s00209-012-1051-7. ISSN 1432-1823.