Topological Duality for Boolean Algebras with a Normal <Emphasis Type="Italic">n</Emphasis>-ary Monotonic Operator |
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Authors: | Sergio Arturo Celani |
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Institution: | (1) CONICET and Departamento de Matemáticas, Facultad de Ciencias Exactas, Univ. Nac. del Centro, Pinto 399, 7000 Tandil, Argentina |
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Abstract: | 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 , such that 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.
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Keywords: | Boolean algebras with a monotonic operator Topological duality Subalgebras Congruences Subdirect irreducibility |
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