ISSN:
1572-9273
Keywords:
Primary 06B10
;
Secondary 08A05
;
Congruence lattice
;
function lattice
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract Thefunction lattice L P is the lattice of all isotone maps from a posetP into a latticeL. D. Duffus, B. Jónsson, and I. Rival proved in 1978 that for afinite poset P, the congruence lattice ofL P is a direct power of the congruence lattice ofL; the exponent is |P|. This result fails for infiniteP. However, utilizing a generalization of theL P construction, theL[D] construction (the extension ofL byD, whereD is a bounded distributive lattice), the second author proved in 1979 that ConL[D] is isomorphic to (ConL) [ConD] for afinite lattice L. In this paper we prove that the isomorphism ConL[D]≅(ConL)[ConD] holds for a latticeL and a bounded distributive latticeD iff either ConL orD is finite.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF02115812
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