This article is cited in 10 papers

Decompositions in Complete Lattices

M. V. Semenova

Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences

Abstract: We give descriptions of lattices that have (unique) irredundant decompositions and decompositions with the replacement property in a class of fully join semidistributive upper continuous lattices and in a class of upper and lower continuous lattices. In particular, it is stated that unique irredundant decompositions in the classes in question coincide with minimal.

Keywords: lattice, semidistributive upper lattice, upper continuous lattice, upper and lower continuous lattice, irredundant decomposition.

UDC: 512.56

Received: 14.04.2000

 English version: Algebra and Logic, 2001, 40:6, 384–390

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