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AAA68: Workshop on General Algebra (68. Arbeitstagung Allgemeine Algebra)
June 10-13, 2004
Technische Universität Dresden
Dresden, Germany |
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Organizers
Reinhard Pöschel, Bernhard Ganter
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Finite lattices as lattices of relative congruences of finite algebras
by
Anvar Nurakunov
Institute of Mathematics, National Academy of Science, Kyrgyz Republic
Let R be quasivariety of algebras, A is algebra from R. A congruence
\theta on A is called R-congruence if A/\theta belongs to R.
The set ConRA of all R-congruences on A forms algebraic lattice
under inclusion. We say that L is lattice of relative congruences if
there exist a quasivariety of algebras R and algebra A in R such that
L is isomorphic to ConRA. It's well-known problem: Is any finite
lattice isomorphic to a lattice of congruences of finite algebra? We show
that for lattices of relative congruences the above problem has positive
solution. Namely, any finite lattice is a lattice of relative congruences of
some finite algebra. In particular, it's true for unars, abelian groups,
semigroups and others.
Date received: May 21, 2004
Copyright © 2004 by the author(s).
The author(s) of this document and the organizers of the conference
have granted their consent to include this abstract in
Atlas Mathematical Conference Abstracts.
Document # canq-86.