κ-Complete Uniquely Complemented Lattices

Order ◽  
2008 ◽  
Vol 25 (2) ◽  
pp. 121-129
Author(s):  
John Harding
Keyword(s):  
Complemented Lattices ◽  
Uniquely Complemented

scholarly journals Unions of uniquely complemented lattices

1997 ◽  
Vol 122 (2) ◽  
pp. 147-152
Author(s):  
Ján Jakubík
Keyword(s):  
Complemented Lattices ◽  
Uniquely Complemented

scholarly journals Congruence Class Sizes in Finite Sectionally Complemented Lattices

2004 ◽  
Vol 47 (2) ◽  
pp. 191-205 ◽  
Author(s):  
G. Grätzer ◽  
E. T. Schmidt
Keyword(s):  
Congruence Class ◽  
Typical Result ◽  
Complemented Lattices ◽  
The Family ◽  
Complemented Lattice ◽  
Congruence Classes

AbstractThe congruences of a finite sectionally complemented lattice L are not necessarily uniform (any two congruence classes of a congruence are of the same size). To measure how far a congruence Θ of L is from being uniform, we introduce Spec Θ, the spectrum of Θ, the family of cardinalities of the congruence classes of Θ. A typical result of this paper characterizes the spectrum S = (mj | j < n) of a nontrivial congruence Θ with the following two properties:

Permutability of Semilattice Congruences on Lattices

1967 ◽  
Vol 19 ◽  
pp. 370-375 ◽  
Author(s):  
Tsuyoshi Fujiwara
Keyword(s):  
Complemented Lattices

Many authors have studied lattice congruences on lattices, but it seems that there are few studies concerning semilattice congruences on lattices. However, it seems that the semilattice congruences on lattices are closely connected with their structure. In this paper, we shall study the characterizations of modular, distributive, and relatively complemented lattices by the permutability of semilattice congruences.We can obtain the dual statements of the following discussion, but we shall not write them as a rule to avoid double descriptions.

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