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Robert Palmer Dilworth (December 2, 1914 – October 29, 1993) was an American mathematician.His primary research area was lattice theory; his biography at the MacTutor History of Mathematics archive states "it would not be an exaggeration to say that he was one of the main factors in the subject moving from being merely a tool of other disciplines to an important subject in its own right".
A lattice is an abstract structure studied in the mathematical subdisciplines of order theory and abstract algebra.It consists of a partially ordered set in which every pair of elements has a unique supremum (also called a least upper bound or join) and a unique infimum (also called a greatest lower bound or meet).
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A number of papers he wrote in the 1930s, culminating in his monograph, Lattice Theory (1940; the third edition remains in print), turned lattice theory into a major branch of abstract algebra. His 1935 paper, "On the Structure of Abstract Algebras" founded a new branch of mathematics, universal algebra.
George A. Grätzer (Hungarian: Grätzer György; born 2 August 1936, in Budapest) is a Hungarian-Canadian mathematician, specializing in lattice theory and universal algebra. He is known for his books on LaTeX [1] and his proof with E. Tamás Schmidt of the Grätzer–Schmidt theorem. [2] [3]
A partially ordered set that is both a join-semilattice and a meet-semilattice is a lattice. A lattice in which every subset, not just every pair, possesses a meet and a join is a complete lattice. It is also possible to define a partial lattice, in which not all pairs have a meet or join but the operations (when defined) satisfy certain axioms ...
In geometry and group theory, a lattice in the real coordinate space is an infinite set of points in this space with the properties that coordinate-wise addition or subtraction of two points in the lattice produces another lattice point, that the lattice points are all separated by some minimum distance, and that every point in the space is within some maximum distance of a lattice point.
In lattice gauge theory, the spacetime is Wick rotated into Euclidean space and discretized into a lattice with sites separated by distance and connected by links. In the most commonly considered cases, such as lattice QCD, fermion fields are defined at lattice sites (which leads to fermion doubling), while the gauge fields are defined on the links.