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Topological Duality for Boolean Algebras with a Normal n-ary Monotonic Operator

机译：具有正态n元单调算子的布尔代数的拓扑对偶

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摘要

In this paper we shall give a topological duality for Boolean algebras endowed with an n-ary monotonic operator (BAMOs). The dual spaces of BAMOs are structures of the form (X, R, τ), such that (X, τ) is a Boolean space, and R is a relation between X and a finite sequences of non-empty closed subsets of X. By means of this duality we shall characterize the equivalence relations of the dual space of a BAMO A that correspond biunivocally to subalgebras of A. We shall prove that there exist bijective correspondences between the lattice of congruences, the lattice of closed filters, and the lattice of certain closed subsets of the dual space of a BAMO. These correspondences are used to study the simple and the subdirectly irreducible algebras.
机译：在本文中，我们将给出具有n元单调算子（BAMO）的布尔代数的拓扑对偶性。 BAMO的对偶空间是（X，R，τ）形式的结构，使得（X，τ）是布尔空间，R是X与X和X的非空闭合子集的有限序列之间的关系。通过这种对偶性，我们将刻画BAMO A的对偶空间的等价关系，该对偶关系与A的子代数单调对应。我们将证明在同余格，封闭滤波器的格和格之间存在双射的对应关系。 BAMO对偶空间的某些封闭子集。这些对应关系用于研究简单和次直接不可约代数。

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