Birkhoff, Garrett Formerly, Department of Mathematics, Harvard University, Cambridge, Massachusetts.
Last reviewed:August 2020
- Kinds of lattices
- Applications to algebra and geometry
- Relation to set theory and logic
- Lattice-ordered groups
- Further applications
- Related Primary Literature
- Additional Reading
Lattice theory deals with properties of order and inclusion, much as group theory treats symmetry. As a generalization of boolean algebra, lattice theory was first applied around 1900 by R. Dedekind to algebraic number theory; however, its recognition as a major branch of mathematics, unifying various aspects of algebra, geometry, and functional analysis, as well as of set theory, logic, and probability (to which boolean algebra had already been applied), dates from the years 1933–1938. See also: Boolean algebra; Group theory; Set theory
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