Lower-modular elements of the lattice of semigroup varieties. II
A semigroup variety is called modular [upper-modular, lowermodular, neutral\ if it is a modular [respectively upper-modular, lowermodular, neutral] element of the lattice of all semigroup varieties. We classify all lower-modular varieties in the class of varieties of semigroups with a completely reg...
Elmentve itt :
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| Dokumentumtípus: | Cikk |
| Megjelent: |
Bolyai Institute, University of Szeged
Szeged
2008
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| Sorozat: | Acta scientiarum mathematicarum
74 No. 3-4 |
| Kulcsszavak: | Matematika |
| Tárgyszavak: | |
| Online Access: | http://acta.bibl.u-szeged.hu/16255 |
| Tartalmi kivonat: | A semigroup variety is called modular [upper-modular, lowermodular, neutral\ if it is a modular [respectively upper-modular, lowermodular, neutral] element of the lattice of all semigroup varieties. We classify all lower-modular varieties in the class of varieties of semigroups with a completely regular power, in the class of varieties of index < 2, and in the class of varieties satisfying an identity of the form xix% • • • xn = xiwx27r • • -xnn, where n is a permutation on the set (1, 2,.. . ,n} with ITT ^ 1 and nn ^ n. It turns out that every lower-modular variety is modular in all these three classes. Moreover, for varieties of index < 2, the properties of being lowermodular, modular and neutral are equivalent. We completely determine also all semigroup varieties that are both upper-modular and lower-modular. It turns out that all such varieties are neutral. |
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| Terjedelem/Fizikai jellemzők: | 539-556 |
| ISSN: | 0001-6969 |