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Commutator-Finite D-Lattices

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Abstract

Commutator-finite D-lattices as a generalization of commutator-finite orthomodular lattices are defined and their properties studied. A necessary and sufficient condition is found under which a D-lattice can be uniquely decomposed into a direct product of an MV-algebra and finitely many irreducible D-lattices which are not MV-algebras. This condition is satisfied if the D-lattice is orthocomplete or if all commutators are sharp. A condition under which a block-finite D-lattice is commutator-finite is found. Some necessary and sufficient conditions for the existence of states and valuations are proved, and some examples are given.

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Authors and Affiliations

  1. Mathematical Institute, Slovak Academy of Sciences, Štefánikova 49, 814 73, Bratislava, Slovakia

    Sylvia Pulmannová

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  1. Sylvia Pulmannová
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Correspondence to Sylvia Pulmannová.

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Mathematics Subject Classifications (2000)

Primary 06F05; Secondary 03G25, 81P10.

This research is supported by grant VEGA 2/3163/23.

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Pulmannová, S. Commutator-Finite D-Lattices. Order 21, 91–105 (2004). https://doi.org/10.1007/s11083-004-5257-0

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  • DOI: https://doi.org/10.1007/s11083-004-5257-0

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