Lattices of lattice homomorphisms

descriptionPublicationkeyboard_double_arrow_right Article 01 Dec 1978 English Publisher:Springer Science and Business Media LLCJournal:Algebra Universalis, volume 8, pages 180-190 (issn: 0002-5270, eissn: 1420-8911,

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Authors: Kucera, T. G.; Sands, B.;

doi: 10.1007/bf02485387

Lattices of lattice homomorphisms

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Abstract

IfL andM are lattices, Hom (L, M) denotes the set of homomorphisms ofL intoM with the pointwise partial order.L is calledcatalytic if Hom (L, M) is a lattice for every latticeM. Among other results, it is shown that every retract of a lattice completely freely generated by a partially ordered set is catalytic, and that every catalytic lattice is semidistributive and satisfies Whitman's condition (W).

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McGill University
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University of Manitoba
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Keywords

Structure theory of lattices

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