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Varieties with modular subalgebra lattices

Published online by Cambridge University Press:  17 April 2009

Trevor Evans  and
Bernhard Ganter
Trevor Evans
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, Arbeitsgruppe 1, Scholobgartenstr. 7, 6100 Darmstadt, Germany.
Bernhard Ganter
Affiliation:
Fachbereich Mathematik, Technische Hochschule Darmstadt, Arbeitsgruppe 1, Scholobgartenstr. 7, 6100 Darmstadt, Germany.
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Abstract

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A classification is begun of varieties of algebras with the property that each algebra in the variety has a modular lattice of subalgebras. This turns out to be a very restrictive condition. Such a variety is hamiltonian. If the algebras in it are idempotent, then it is a variety of sets. A variety is subalgebra-modular if and only if it is hamiltonian and satisfies certain conditions on the terms in its three generator free algebras.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 28 , Issue 2 , October 1983 , pp. 247 - 254
Copyright
Copyright © Australian Mathematical Society 1983

References

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