Bousfield class

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: ${\displaystyle X\otimes Y=0}$. 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.