Varieties of Distributive Lattices with Unary Operations II

H.A. Priestley and R. Santos

Abstract: This paper extends to the general setting of [11], [25] procedures presented earlier for varieties of Ockham algebras. Given a suitable finitely generated variety $\Cal A$ of distributive-lattice-ordered algebras with unary operations, in which the subdirectly irreducible algebras are assumed to have been pre-determined, a natural duality, free algebras and coproducts can be obtained algorithmically for any prescribed subvariety of $\Cal A$. Further, the meet-irreducible members of the lattice of equational theories of $\Cal A$ can be written down. The theory is illustrated by carrying this programme through for varieties of double $\scat{MS}$-algebras.

Keywords: Natural duality; Priestley duality; free algebra; double MS-algebra.

Classification (MSC2000): 06D05, 06D25, 03G20, 08B99

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