PROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICES
A bounded distributive lattice L has two unital semilattice reducts, denoted L̂^ and Lv. These ordered structures have a common canonical extension Lδ. As algebras, they also possess profinite completions, L̂, L̂^ and L̂v; the first of these is well known to coincide with Lδ. Depending on the struct...
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| Format: | Journal article |
| Language: | English |
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2013
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| _version_ | 1797093256210677760 |
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| author | Gouveia, M Priestley, H |
| author_facet | Gouveia, M Priestley, H |
| author_sort | Gouveia, M |
| collection | OXFORD |
| description | A bounded distributive lattice L has two unital semilattice reducts, denoted L̂^ and Lv. These ordered structures have a common canonical extension Lδ. As algebras, they also possess profinite completions, L̂, L̂^ and L̂v; the first of these is well known to coincide with Lδ. Depending on the structure of L, these three completions may coincide or may be di erent. Necessary and sufficient conditions are obtained for the canonical extension of L to coincide with the profinite completion of one, or of each, of its semilattice reducts. The techniques employed here draw heavily on duality theory and on results from the theory of continuous lattices. © 2013 University of Houston. |
| first_indexed | 2024-03-07T03:57:41Z |
| format | Journal article |
| id | oxford-uuid:c36e626d-31cb-4005-854b-1d5e0b584c4d |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T03:57:41Z |
| publishDate | 2013 |
| record_format | dspace |
| spelling | oxford-uuid:c36e626d-31cb-4005-854b-1d5e0b584c4d2022-03-27T06:16:19ZPROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICESJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:c36e626d-31cb-4005-854b-1d5e0b584c4dEnglishSymplectic Elements at Oxford2013Gouveia, MPriestley, HA bounded distributive lattice L has two unital semilattice reducts, denoted L̂^ and Lv. These ordered structures have a common canonical extension Lδ. As algebras, they also possess profinite completions, L̂, L̂^ and L̂v; the first of these is well known to coincide with Lδ. Depending on the structure of L, these three completions may coincide or may be di erent. Necessary and sufficient conditions are obtained for the canonical extension of L to coincide with the profinite completion of one, or of each, of its semilattice reducts. The techniques employed here draw heavily on duality theory and on results from the theory of continuous lattices. © 2013 University of Houston. |
| spellingShingle | Gouveia, M Priestley, H PROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICES |
| title | PROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICES |
| title_full | PROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICES |
| title_fullStr | PROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICES |
| title_full_unstemmed | PROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICES |
| title_short | PROFINITE COMPLETIONS AND CANONICAL EXTENSIONS OF SEMILATTICE REDUCTS OF DISTRIBUTIVE LATTICES |
| title_sort | profinite completions and canonical extensions of semilattice reducts of distributive lattices |
| work_keys_str_mv | AT gouveiam profinitecompletionsandcanonicalextensionsofsemilatticereductsofdistributivelattices AT priestleyh profinitecompletionsandcanonicalextensionsofsemilatticereductsofdistributivelattices |