Title: | On congruences of $G$-sets (English) |

Author: | Vernikov, B. M. |

Language: | English |

Journal: | Commentationes Mathematicae Universitatis Carolinae |

ISSN: | 0010-2628 (print) |

ISSN: | 1213-7243 (online) |

Volume: | 38 |

Issue: | 3 |

Year: | 1997 |

Pages: | 603-613 |

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Category: | math |

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Summary: | We describe $G$-sets whose congruences satisfy some natural lattice or multiplicative restrictions. In particular, we determine $G$-sets with distributive, arguesian, modular, upper or lower semimodular congruence lattice as well as congruence $n$-permutable $G$-sets for $n=2,2.5,3$. (English) |

Keyword: | $G$-set |

Keyword: | congruence lattice |

Keyword: | congruence distributivity |

Keyword: | congruence modularity |

Keyword: | congruence $n$-permutability |

MSC: | 08A30 |

MSC: | 08A60 |

idZBL: | Zbl 0938.08002 |

idMR: | MR1485081 |

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Date available: | 2009-01-08T18:36:46Z |

Last updated: | 2012-04-30 |

Stable URL: | http://hdl.handle.net/10338.dmlcz/118958 |

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Reference: | [9] Vernikov B.M., Volkov M.V.: Commutative semigroup varieties with modular subvariety lattices.in: J. Rhodes (ed.), Monoids and Semigroups with Applications, World Scientific, Singapore, 1991, pp. 233-253. Zbl 0797.20047, MR 1142380 |

Reference: | [10] Vernikov B.M., Volkov M.V.: Structure of lattices of nilpotent semigroup varieties.in: C. Bonzini, A. Cherubini and C. Tibiletti (eds.), Semigroups. Algebraic Theory and Applications to Formal Languages and Codes, World Scientific, Singapore, 1993, pp. 297-299. Zbl 0813.20064, MR 1647267 |

Reference: | [11] Vernikov B.M., Volkov M.V.: Lattices of nilpotent semigroup varieties. II.Izv. Ural State University, Ser. Matem., Mechan., accepted Russian. |

Reference: | [12] Vernikov B.M., Volkov M.V.: Semimodular varieties of semigroups.to appear. MR 1001692 |

Reference: | [13] Vernikov B.M., Volkov M.V.: Permutability of fully invariant congruences on relatively free semigroups.Acta Sci. Math. (Szeged), submitted. Zbl 0889.20031 |

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Reference: | [15] Volkov M.V.: Semigroup varieties with commuting fully invariant congruences on free objects.Contemp. Math. 131 part 3 (1992), 295-316. Zbl 0768.20025, MR 1175889 |

Reference: | [16] Volkov M.V.: Young diagrams and the structure of the lattice of overcommutative semigroup varieties.in: P.M. Higgins (ed.), Transformation Semigroups, Proc. Int. Conf. held at the Univ. Essex, Univ. Essex, Colchester, 1994, pp.99-110. Zbl 0880.20042, MR 1491912 |

Reference: | [17] Volkov M.V.: Identities in the Lattice of Semigroup Varieties.Doctor Sci. Dissertation, St. Petersburg, 1994 Russian. |

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