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Lattices, Universal Algebra and Applications
May 28-30, 2003
Centro de Algebra da Universidade de Lisboa
Lisbon, Portugal

Organizers
Gabriela Bordalo, Isabel Ferreirim, Maria Joao Saramago, Luis Sequeira

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Functional representation of lattices
by
Branimir Seselja
University of Novi Sad

A mapping from a nonempty set to a lattice L produces a collection of subsets of S which is a lattice under inclusion. The latter is isomorphic to a quotient of L under a closure operator on L. Necessary and sufficient conditions under which two mappings from S to L produce equal collections of subsets (hence isomorphic quotients of L) are given. Equality of quotients induces an equivalence relation E on the lattice LS of all mappings from S to L. Conditions under which LS/E is a lattice under inclusion are given. An analogue functional representation of posets will also be presented.

Date received: February 27, 2003

Copyright © 2003 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 # cajs-22.