This article is cited in 1 paper

Decompositions in complete lattices. II. Replaceable irredundant decompositions

M. V. Schwidefsky<sup>ab

a</sup> Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
^b Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia

Abstract: A characterization of lattices with replaceable irredundant decompositions is given in the following six classes:
– the class of upper and lower continuous lattices;
– the class of upper continuous join-semidistributive lattices;
– the class of upper semimodular lower continuous lattices;
– the class of upper semimodular join-semidistributive lattices;
– the class of consistent lower continuous lattices;
– the class of consistent join-semidistributive lattices.

Keywords: consistent lattice, irredundant decomposition, join-semidistributive, lattice, lower continuous, semimodular, strongly atomic, upper continuous, weakly atomic.

UDC: 512.56

Received: 05.04.2016
Revised: 10.11.2016

DOI: 10.17377/alglog.2017.56.305

 English version: Algebra and Logic, 2017, 56:3, 236–244

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