Discrete dualities for n-potent MTL-algebras and 2-potent BL-algebras

Discrete dualities are developed for n-potent MTL-algebras and for 2-potent BL-algebras. That is, classes of frames, or relational systems, are defined that serve as dual counterparts to these classes of algebras. The frames defined here are extensions of the frames that were developed for MTL-algebras in [24] and [25]; the additional frame conditions required are given here and also the proofs that discrete dualities hold with respect to such frames. The duality also provides an embedding from an n-potent MTL-algebra, or 2-potent BL-algebra, into the complex algebra of its canonical frame, which is a complete algebra in the lattice sense.