Lattices
In this video, we introduce the notion of a lattice, a set equipped with binary operations which are associative and commutative, all elements are idempotent with respect to both operations, and the two operations mutually absorb each other. This generalizes the notion of a collection of sets equipped with the union and intersection operations. We prove that lattices always form a natural partially ordered set for which one operation gives the least upper bound and the other operation gives the greatest lower bound. We present the Principle of Duality for lattices.
This is lecture 37 (part 2/2) of the lecture series offered by Dr. Andrew Misseldine for the course Math 4230 - Abstract Algebra II at Southern Utah University. A transcript of this lecture can be found at Dr. Misseldine's website or through his Google Drive at:
https://drive.google.com/file/d/1QVkL...
This lecture is based upon Sections 19.1 of Abstract Algebra: Theory and Applications (http://abstract.ups.edu/) by Tom Judson. Please post any questions you might have below in the comment field and Dr. Misseldine (or other commenters) can answer them for you. Please also subscribe for further updates.