On minimal simple lattices
Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices...
Ausführliche Beschreibung
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| Autor*in: |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
1994 |
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| Umfang: |
41 |
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| Reproduktion: |
Springer Online Journal Archives 1860-2002 |
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| Übergeordnetes Werk: |
in: Algebra universalis - 1971, 32(1994) vom: Jan., Seite 63-103 |
| Übergeordnetes Werk: |
volume:32 ; year:1994 ; month:01 ; pages:63-103 ; extent:41 |
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| 520 | |a Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. | ||
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(DE-627)NLEJ189142863 DE-627 ger DE-627 rakwb eng On minimal simple lattices 1994 41 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. Springer Online Journal Archives 1860-2002 McKenzie, R. oth in Algebra universalis 1971 32(1994) vom: Jan., Seite 63-103 (DE-627)NLEJ188985026 (DE-600)1463841-1 1420-8911 nnns volume:32 year:1994 month:01 pages:63-103 extent:41 http://dx.doi.org/10.1007/BF01190817 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 32 1994 1 63-103 41 |
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(DE-627)NLEJ189142863 DE-627 ger DE-627 rakwb eng On minimal simple lattices 1994 41 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. Springer Online Journal Archives 1860-2002 McKenzie, R. oth in Algebra universalis 1971 32(1994) vom: Jan., Seite 63-103 (DE-627)NLEJ188985026 (DE-600)1463841-1 1420-8911 nnns volume:32 year:1994 month:01 pages:63-103 extent:41 http://dx.doi.org/10.1007/BF01190817 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 32 1994 1 63-103 41 |
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(DE-627)NLEJ189142863 DE-627 ger DE-627 rakwb eng On minimal simple lattices 1994 41 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. Springer Online Journal Archives 1860-2002 McKenzie, R. oth in Algebra universalis 1971 32(1994) vom: Jan., Seite 63-103 (DE-627)NLEJ188985026 (DE-600)1463841-1 1420-8911 nnns volume:32 year:1994 month:01 pages:63-103 extent:41 http://dx.doi.org/10.1007/BF01190817 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 32 1994 1 63-103 41 |
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(DE-627)NLEJ189142863 DE-627 ger DE-627 rakwb eng On minimal simple lattices 1994 41 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. Springer Online Journal Archives 1860-2002 McKenzie, R. oth in Algebra universalis 1971 32(1994) vom: Jan., Seite 63-103 (DE-627)NLEJ188985026 (DE-600)1463841-1 1420-8911 nnns volume:32 year:1994 month:01 pages:63-103 extent:41 http://dx.doi.org/10.1007/BF01190817 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 32 1994 1 63-103 41 |
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(DE-627)NLEJ189142863 DE-627 ger DE-627 rakwb eng On minimal simple lattices 1994 41 nicht spezifiziert zzz rdacontent nicht spezifiziert z rdamedia nicht spezifiziert zu rdacarrier Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. Springer Online Journal Archives 1860-2002 McKenzie, R. oth in Algebra universalis 1971 32(1994) vom: Jan., Seite 63-103 (DE-627)NLEJ188985026 (DE-600)1463841-1 1420-8911 nnns volume:32 year:1994 month:01 pages:63-103 extent:41 http://dx.doi.org/10.1007/BF01190817 GBV_USEFLAG_U ZDB-1-SOJ GBV_NL_ARTICLE AR 32 1994 1 63-103 41 |
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in Algebra universalis 32(1994) vom: Jan., Seite 63-103 volume:32 year:1994 month:01 pages:63-103 extent:41 |
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Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. |
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Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. |
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Abstract The class of simple lattices, excluding the two-element lattice, is preordered by placing L0≤L1 iff L0 belongs to the variety generated by L1. We prove that the finite simple lattices minimal under this pre-ordering generate the variety of all lattices. We construct infinite simple lattices minimal under the ordering, and others that contain, in the sense of the ordering, no minimal simple lattices. |
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