On complete congruence lattices of complete lattices-Reference-Cited by-同舟云学术

On complete congruence lattices of complete lattices

Published:1991 Issue:1 Volume:327 Page:385-405
ISSN:0002-9947
Container-title:Transactions of the American Mathematical Society
language:en
Short-container-title:Trans. Amer. Math. Soc.

Author:

Grätzer G.,Lakser H.

Abstract

The lattice of all complete congruence relations of a complete lattice is itself a complete lattice. In this paper, we characterize this lattice as a complete lattice. In other words, for a complete lattice L L , we construct a complete lattice K K such that L L is isomorphic to the lattice of complete congruence relations of K K . Regarding K K as an infinitary algebra, this result strengthens the characterization theorem of congruence lattices of infinitary algebras of G. Grätzer and W. A. Lampe. In addition, we show how to construct K K so that it will also have a prescribed automorphism group.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/tran/1991-327-01/S0002-9947-1991-1036003-5/S0002-9947-1991-1036003-5.pdf

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