Previous |  Up |  Next

Article

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
.
Category: math
.
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
.
Date available: 2009-01-08T18:36:46Z
Last updated: 2012-04-30
Stable URL: http://hdl.handle.net/10338.dmlcz/118958
.
Reference: [1] Berman J.: On the congruence lattices of unary algebras.Proc. Amer. Math. Soc. 36 (1972), 34-38. Zbl 0249.08002, MR 0309833
Reference: [2] Crawley P., Dilworth R.P.: Algebraic Theory of Lattices.Prentice-Hall, 1973. Zbl 0494.06001
Reference: [3] Egorova D.P.: Unars with the congruence lattice of a special kind.in: V.V. Vagner (ed.), Investigations in Algebra, Saratov State University, Saratov 5 (1977), pp.3-19 Russian. MR 0491412
Reference: [4] Egorova D.P.: The congruence lattice of unary algebra.in: V.N. Salii (ed.), Ordered Sets and Lattices, Saratov State University, Saratov 5 (1978), pp.11-44 Russian. MR 0547294
Reference: [5] Egorova D.P., Skornjakov L.A.: On the congruence lattice of unary algebra.in: V.N. Salii (ed.), Ordered Sets and Lattices, Saratov State University, Saratov 4 (1977), pp.28-40 Russian. MR 0480280
Reference: [6] McKenzie R.N., McNulty G.F., Taylor W.F.: Algebras. Lattices. Varieties.Vol. I, Wadsworth & Brooks/Cole, Monterey, 1987. Zbl 0611.08001, MR 0883644
Reference: [7] Skornjakov L.A.: Unars.Colloq. Math. Soc. J. Bolyai 29 (1982), 735-743. Zbl 0504.08006, MR 0660907
Reference: [8] Vernikov B.M.: Distributivity, modularity, and related conditions in lattices of overcommutative semigroup varieties.Proc. Int. Conf. ``Semigroups and their Applications, including Semigroup Rings'', accepted. Zbl 0970.20037
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
Reference: [14] Volkov M.V.: Commutative semigroup varieties with distributive subvariety lattices.Contrib. to General Algebra 7 (1991), 351-359. Zbl 0762.20022, MR 1143098
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.
.

Files

Files Size Format View
CommentatMathUnivCarolRetro_38-1997-3_17.pdf 236.8Kb application/pdf View/Open
Back to standard record
Partner of
EuDML logo