Dualities for some De Morgan algebras with operators and Lukasiewicz algebras

Source abstract

Abstract Algebras ( A , ∧, ∨, ~, γ, 0, 1) of type (2,2,1,1,0,0) such that (A, ∧, ∨, ~, γ 0, 1) is a De Morgan algebra and γ is a lattice homomorphism from A into its center that satisfies one of the conditions (i) a ≤ γ a or (ii) a ≤ ~ a ∧ γ a are considered. The dual categories and the lattice of their subvarieties are determined, and applications to Lukasiewicz algebras are given.