Partition-induced natural dualities for varieties of pseudo- complemented distributive lattices
A natural duality is obtained for each finitely generated variety Bn (n < ω) of distributive p-algebras. The duality for Bn is based on a schizophrenic object: P-1 in Bn is the algebra 2n ⊕ 1 which generates the variety and P-1 is a topological relational structure carrying the discrete topol...
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| Format: | Journal article |
| Language: | English |
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1993
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| _version_ | 1826287171918626816 |
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| author | Davey, B Priestley, H |
| author_facet | Davey, B Priestley, H |
| author_sort | Davey, B |
| collection | OXFORD |
| description | A natural duality is obtained for each finitely generated variety Bn (n < ω) of distributive p-algebras. The duality for Bn is based on a schizophrenic object: P-1 in Bn is the algebra 2n ⊕ 1 which generates the variety and P-1 is a topological relational structure carrying the discrete topology and a set of algebraic relations. The relations are (i) the graphs of a (3-element) generating set for the endomorphism monoid of P-1 and (ii) a set of subalgebras of P2-2 in one-to-one correspondence with partitions of the integer n. Each of the latter class of relations, regarded as a digraph, is 'nearly' the union of two isomorphic trees. The duality is obtained by the piggyback method of Davey and Werner (which has previously yielded a duality in case n ≤ 2), combined with use of the restriction to finite p-algebras of the duality for bounded distributive lattices, which enables the relations suggested by the general theory to be concretely described. © 1993. |
| first_indexed | 2024-03-07T01:54:38Z |
| format | Journal article |
| id | oxford-uuid:9b47b6d1-18d4-4aa9-965c-a97a489d6622 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T01:54:38Z |
| publishDate | 1993 |
| record_format | dspace |
| spelling | oxford-uuid:9b47b6d1-18d4-4aa9-965c-a97a489d66222022-03-27T00:27:42ZPartition-induced natural dualities for varieties of pseudo- complemented distributive latticesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:9b47b6d1-18d4-4aa9-965c-a97a489d6622EnglishSymplectic Elements at Oxford1993Davey, BPriestley, HA natural duality is obtained for each finitely generated variety Bn (n < ω) of distributive p-algebras. The duality for Bn is based on a schizophrenic object: P-1 in Bn is the algebra 2n ⊕ 1 which generates the variety and P-1 is a topological relational structure carrying the discrete topology and a set of algebraic relations. The relations are (i) the graphs of a (3-element) generating set for the endomorphism monoid of P-1 and (ii) a set of subalgebras of P2-2 in one-to-one correspondence with partitions of the integer n. Each of the latter class of relations, regarded as a digraph, is 'nearly' the union of two isomorphic trees. The duality is obtained by the piggyback method of Davey and Werner (which has previously yielded a duality in case n ≤ 2), combined with use of the restriction to finite p-algebras of the duality for bounded distributive lattices, which enables the relations suggested by the general theory to be concretely described. © 1993. |
| spellingShingle | Davey, B Priestley, H Partition-induced natural dualities for varieties of pseudo- complemented distributive lattices |
| title | Partition-induced natural dualities for varieties of pseudo- complemented distributive lattices |
| title_full | Partition-induced natural dualities for varieties of pseudo- complemented distributive lattices |
| title_fullStr | Partition-induced natural dualities for varieties of pseudo- complemented distributive lattices |
| title_full_unstemmed | Partition-induced natural dualities for varieties of pseudo- complemented distributive lattices |
| title_short | Partition-induced natural dualities for varieties of pseudo- complemented distributive lattices |
| title_sort | partition induced natural dualities for varieties of pseudo complemented distributive lattices |
| work_keys_str_mv | AT daveyb partitioninducednaturaldualitiesforvarietiesofpseudocomplementeddistributivelattices AT priestleyh partitioninducednaturaldualitiesforvarietiesofpseudocomplementeddistributivelattices |