The Complete Congruence Lattice of a Complete Lattice

G. Grätzer
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G. Grätzer: University of Manitoba, Department of Mathematics

A chapter in Lattices, Semigroups, and Universal Algebra, 1990, pp 81-87 from Springer

Abstract: Abstract G. Birkhoff [1] raised the following question in 1945: Is every complete lattice isomorphic to the lattice of congruence relations of a suitable (infinitary) algebra? In 1948, Birkhoff restated this question in the Second Edition of his Lattice Theory [2]; however, “(infinitary)” was dropped from the question. This was intentional; G. Birkhoff referred to some continuity conditions that must hold in a congruence lattice of a (finitary) algebra.

Date: 1990
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DOI: 10.1007/978-1-4899-2608-1_9

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