Abstract
In Chapter 10, we proved that every finite distributive lattice D can be represented as the congruence lattice of a finite semimodular lattice L of size O(n 3). In this chapter we discuss what can we say about rectangular lattices, which form a very small subclass of semimodular lattices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Bibliography
_________ , Planar Semimodular Lattices: Congruences. Chapter 4 in LTS1.
_________ , Notes on planar semimodular lattices. III. Rectangular lattices. Acta Sci. Math. ( Szeged ) 75 (2009), 29–48.
_________ , Notes on planar semimodular lattices. IV. The size of a minimal congruence lattice representation with rectangular lattices. Acta Sci. Math. ( Szeged ) 76 (2010), 3–26.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Grätzer, G. (2016). Rectangular Lattices. In: The Congruences of a Finite Lattice. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-38798-7_11
Download citation
DOI: https://doi.org/10.1007/978-3-319-38798-7_11
Published:
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-38796-3
Online ISBN: 978-3-319-38798-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)