The usual axiomatization of residuated lattices involve using ≤. I know I can expand away the use of ≤ using a definition such as (x ≤ y) := (x ∧ y = x), but I fear I will get a set of messy axioms.

What is a nice equational axiomatization of residuated lattices for the signature (U, ∧, ∨, •, e, /, \) (or any other signature if you prefer)?