The order of principal congruences of a bounded lattice
G. Gr\"atzer
TL;DR
This paper characterizes the structure of the order of principal congruences in bounded lattices, including complete lattices and those of length 5, and discusses open problems in this area.
Contribution
It provides a characterization of the order of principal congruences in bounded lattices and introduces new open problems in the field.
Findings
Order of principal congruences characterized as a bounded ordered set
Extension of characterization to complete lattices and lattices of length 5
Presentation of open problems in the study of principal congruences
Abstract
We characterize the order of principal congruences of a bounded lattice (also of a complete lattice and of a lattice of length 5) as a bounded ordered set. We also state a number of open problems in this new field.
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Taxonomy
TopicsAdvanced Algebra and Logic