Vol. 73, No. 1, 1977

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Complemented congruences on complemented lattices

Melvin F. Janowitz

Vol. 73 (1977), No. 1, 87–90

We prove that a congruence relation on a complemented lattice has a complement if and only if it is the minimal congruence generated by a central element. This result is then used to show that a complemented lattice has a Boolean lattice of congruence relations if and only if it is the direct product of a finite number of simple lattices. It is also used to obtain some information on the structure of complemented lattices whose lattice of congruences is a Stone lattice.

Mathematical Subject Classification
Primary: 06A25, 06A25
Received: 17 June 1976
Revised: 3 May 1977
Published: 1 November 1977
Melvin F. Janowitz