Duals of Simple and Subdirectly Irreducible Distributive Modal Algebras

摘要

Simplicity and subdirect irreducibility of complex algebra duals of Kripke frames can be readily characterized in terms of roots of the corresponding Kripke frames.Here these characterizations are generalized to the case of distributive modal algebras (A, ∨, ∧, 0,1, ◇, □, (▽),(△)), and their duals. Such an algebra consists of a distributive bounded lattice (A, ∧, ∨,0,1) together with a join preserving operator ◇, a meet preserving operator □, a join reversing operator (▽), and a meet reversing operator (△).