Commutator-finite orthomodular lattices |
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Authors: | Richard Greechie Louis Herman |
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Institution: | (1) Department of Mathematics, Kansas State University, 66506 Manhattan, KS, USA |
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Abstract: | The class
of orthomodular lattices which have only finitely many commutators is investigated. The following theorems are proved:
contains the block-finite orthomodular lattices. Every irreducible element of
is simple. Every element of
is a direct product of a Boolean algebra and finitely many simple orthomodular lattices. The irreducible elements of
which are modular, or are M-symmetric with at least one atom, have height two or less. |
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Keywords: | 06C15 |
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