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.

中文翻译：

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MV 代数及其他领域的 Priestley 对偶性

我们为配备二元双准算子的一大类分配格提供了关于扩展 Priestley 对偶性的新视角。在这种方法下，非晶格二元运算均表示为对偶空间上的一对部分二元运算。在这个丰富的环境中，对偶代数方面的方程条件可能更常被呈现为对偶空间上的一阶条件。特别是，我们将我们的一般结果专门用于各种 MV-代数，获得这些的对偶性，其中公理化 MV-代数的方程被二元化为一阶条件。