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Complete congruences on lattices of varieties and of pseudovarieties


Trotter, PG and Pastijn, F, Complete congruences on lattices of varieties and of pseudovarieties, International Journal of Algebra and Computation, 8, (2) pp. 171-201. ISSN 0218-1967 (1998) [Refereed Article]

DOI: doi:10.1142/S0218196798000107


Three methods for the construction of all complete congruences on the lattice Lv(V) of subvarieties of a variety V are introduced. It is shown that there exists an order preserving embedding of the lattice of complete congruences on the lattice Lp(P) of all subpseudovarieties of a given pseudovariety P into the direct product of the lattices of complete congruences on lattices of subvarieties of varieties generated by members of P; thus there are methods for constructing all complete congruences on Lp(P). By way of application, 2אo complete congruences and complete endomorphisms are constructed on any lattice Lv(V), where V is a certain epigroup variety which includes all bands; there is an analogous application for the lattice of all pseudovarieties of semigroups.

Item Details

Item Type:Refereed Article
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Algebra and number theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Trotter, PG (Dr Peter Trotter)
UTAS Author:Pastijn, F (Professor Francis Pastijn)
ID Code:14031
Year Published:1998
Web of Science® Times Cited:9
Deposited By:Mathematics
Deposited On:1998-08-01
Last Modified:2011-08-09

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