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On the relation of a distributive lattice to its lattice of ideals

Published online by Cambridge University Press:  17 April 2009

Herbert S. Gaskill
Herbert S. Gaskill
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbla, Canada.
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Abstract

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In this note we examine the relationship of a distributive lattice to its lattice of ideals. Our main result is that a distributive lattice and its lattice of ideals share exactly the same collection of finite sublattices. In addition we give a related result characterizing those finite distributive lattices L which can be embedded in a lattice L′ whenever they can be embedded in its lattice of ideals T(L′).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 377 - 385
Copyright
Copyright © Australian Mathematical Society 1972

References

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