Involutive Residuated Lattices Based on Modular and Distributive Lattices
Abstract An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic con...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Olson, Jeffrey S. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2013 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media Dordrecht 2013 |
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| Übergeordnetes Werk: |
Enthalten in: Order - Springer Netherlands, 1984, 31(2013), 3 vom: 30. Okt., Seite 373-389 |
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| Übergeordnetes Werk: |
volume:31 ; year:2013 ; number:3 ; day:30 ; month:10 ; pages:373-389 |
| Links: |
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| DOI / URN: |
10.1007/s11083-013-9307-3 |
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| 520 | |a Abstract An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic conditions. A classification of all IRLs based on the modular lattices Mn is provided. | ||
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10.1007/s11083-013-9307-3 doi (DE-627)OLC2074605145 (DE-He213)s11083-013-9307-3-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Olson, Jeffrey S. verfasserin aut Involutive Residuated Lattices Based on Modular and Distributive Lattices 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic conditions. A classification of all IRLs based on the modular lattices Mn is provided. Involutive residuated lattice Involution Modular lattice Enthalten in Order Springer Netherlands, 1984 31(2013), 3 vom: 30. Okt., Seite 373-389 (DE-627)130333581 (DE-600)591930-7 (DE-576)015892093 0167-8094 nnns volume:31 year:2013 number:3 day:30 month:10 pages:373-389 https://doi.org/10.1007/s11083-013-9307-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2088 GBV_ILN_4036 AR 31 2013 3 30 10 373-389 |
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10.1007/s11083-013-9307-3 doi (DE-627)OLC2074605145 (DE-He213)s11083-013-9307-3-p DE-627 ger DE-627 rakwb eng 510 VZ 17,1 ssgn Olson, Jeffrey S. verfasserin aut Involutive Residuated Lattices Based on Modular and Distributive Lattices 2013 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media Dordrecht 2013 Abstract An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic conditions. A classification of all IRLs based on the modular lattices Mn is provided. Involutive residuated lattice Involution Modular lattice Enthalten in Order Springer Netherlands, 1984 31(2013), 3 vom: 30. Okt., Seite 373-389 (DE-627)130333581 (DE-600)591930-7 (DE-576)015892093 0167-8094 nnns volume:31 year:2013 number:3 day:30 month:10 pages:373-389 https://doi.org/10.1007/s11083-013-9307-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-MAT SSG-OPC-MAT GBV_ILN_40 GBV_ILN_70 GBV_ILN_2004 GBV_ILN_2088 GBV_ILN_4036 AR 31 2013 3 30 10 373-389 |
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Abstract An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic conditions. A classification of all IRLs based on the modular lattices Mn is provided. © Springer Science+Business Media Dordrecht 2013 |
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Abstract An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic conditions. A classification of all IRLs based on the modular lattices Mn is provided. © Springer Science+Business Media Dordrecht 2013 |
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Abstract An involutive residuated lattice (IRL) is a lattice-ordered monoid possessing residual operations and a dualizing element. We show that a large class of self-dual lattices may be endowed with an IRL structure, and give examples of lattices which fail to admit IRLs with natural algebraic conditions. A classification of all IRLs based on the modular lattices Mn is provided. © Springer Science+Business Media Dordrecht 2013 |
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