We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.
Priestley duality for MV-algebras and beyond / W. Fussner, M. Gehrke, S.J. Van Gool, V. Marra. - In: FORUM MATHEMATICUM. - ISSN 0933-7741. - 33:4(2021 Jul 01), pp. 899-921. [10.1515/forum-2020-0115]
Priestley duality for MV-algebras and beyond
V. Marra
2021
Abstract
We provide a new perspective on extended Priestley duality for a large class of distributive lattices equipped with binary double quasioperators. Under this approach, non-lattice binary operations are each presented as a pair of partial binary operations on dual spaces. In this enriched environment, equational conditions on the algebraic side of the duality may more often be rendered as first-order conditions on dual spaces. In particular, we specialize our general results to the variety of MV-algebras, obtaining a duality for these in which the equations axiomatizing MV-algebras are dualized as first-order conditions.File | Dimensione | Formato | |
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