On the direct product decomposition of lattices
by
Sándor Radeleczki
Mathematical Institute, University of Miskolc, Hungary

We prove necessary and sufficient conditions for the direct decomposition of a bounded lattice into the product of directly indecomposable lattices. In the case of a complete lattice L, these conditions can be replaced with equivalent conditions on the set of central-prime elements of L, or with other equivalent conditions concerning the centre of the tolerance lattice of L. We prove that a complete lattice L is a direct product of directly indecomposable lattices if and only if it can be represented as a concept lattice of a clarified context K having the property that any direct product decomposition L = L₁ ×L₂ induces a decomposition of the context K into a direct sum K=K₁+K₂ such that L = L(K₁) ×L(K₂).

Date received: June 6, 2002

Copyright © 2002 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 Conferences Inc. Document # caiv-20.