Freely generated lattices

Rosie Laking (University of Manchester, School of Mathematics)

G.114, Alan Turing Building,

This talk will introduce the basics of abstract lattice theory with a view to understanding the following theorem due to G. Birkhoff (1940):

Theorem: Let \(L\) be a modular lattice and let \(C_1\) and \(C_2\) be chains in \(L\). Then the sublattice of \(L\) generated by the union of \(C_1\) and \(C_2\) is distributive.

The journey to understanding this theorem will take us via the concept of free lattices, including a nice pictorial description of the free lattice (over the variety of modular lattices) generated by the union of two chains.

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