This paper applies a combination of algebraic and topological methods to obtain new structural results on mp- purified residuated lattices. It is demonstrated that mp-residuated lattices are strongly tied up with the dual hull-kernel topology. Mainly, it shown lattice mp if only its minimal prime spectrum, equipped topology, Hausdorff fitted normal. For $${\mathfrak {A}}$$ subalgebra {S}}$$ , n...