  In this paper we define the Boolean Lifting Property (BLP) for residuated
lattices to be the property that all Boolean elements can be lifted modulo
every filter, and study residuated lattices with BLP. Boolean algebras, chains,
local and hyperarchimedean residuated lattices have BLP. BLP behaves
interestingly in direct products and involutive residuated lattices, and it is
closely related to arithmetic properties involving Boolean elements, nilpotent
elements and elements of the radical. When BLP is present, strong
representation theorems for semilocal and maximal residuated lattices hold.
