Small sublattices with large dominions (Q2491961)
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scientific article
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Small sublattices with large dominions |
scientific article |
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Small sublattices with large dominions (English)
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31 May 2006
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For a subalgebra \(A\) of an algebra \(B\) in a given class, the dominion of \(A\) in \(B\) consists of all \(x\) which are identified under all homomorphisms coninciding on \(A\). It is shown that, within a finitely generated lattice variety, finite sublattices may not have infinite dominions. Counterxamples are given for the variety generated by modular lattices of width 4 and for the variety generated by some orthomodular lattice.
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dominion
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nonsurejective epimorphism
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finitely generated lattice variety
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orthomodular lattice
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modular lattice
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