In mathematics, a dyadic rational or binary rational is a number that can be expressed as a fraction whose denominator is a power of two. For example, 1/2, 3/2, and 3/8 are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations. Dyadic rationals also have applications in weights and measures, musical time signatures, and early mathematics education. They can accurately approximate any real number.
In the area of modern algebra known as group theory, the Rudvalis groupRu is a sporadic simple group of order
Robert Louis Griess, Jr. is a mathematician working on finite simple groups and vertex algebras. He is currently the John Griggs Thompson Distinguished University Professor of mathematics at University of Michigan.
George Isaac Glauberman is a mathematician at the University of Chicago who works on finite simple groups. He proved the ZJ theorem and the Z* theorem.
In mathematics, the congruence lattice problem asks whether every algebraic distributive lattice is isomorphic to the congruence lattice of some other lattice. The problem was posed by Robert P. Dilworth, and for many years it was one of the most famous and long-standing open problems in lattice theory; it had a deep impact on the development of lattice theory itself. The conjecture that every distributive lattice is a congruence lattice is true for all distributive lattices with at most ℵ1 compact elements, but F. Wehrung provided a counterexample for distributive lattices with ℵ2 compact elements using a construction based on Kuratowski's free set theorem.
Richard Gordon Swan is an American mathematician who is known for the Serre–Swan theorem relating the geometric notion of vector bundles to the algebraic concept of projective modules, and for the Swan representation, an l-adic projective representation of a Galois group. His work has mainly been in the area of algebraic K-theory.
In mathematics, the concept of groupoid algebra generalizes the notion of group algebra.
In mathematics, the Alvis–Curtis duality is a duality operation on the characters of a reductive group over a finite field, introduced by Charles W. Curtis and studied by his student Dean Alvis. Kawanaka introduced a similar duality operation for Lie algebras.
In mathematics, Nakayama's conjecture is a conjecture about Artinian rings, introduced by Nakayama. The generalized Nakayama conjecture is an extension to more general rings, introduced by Auslander and Reiten. Leuschke & Huneke (2004) proved some cases of the generalized Nakayama conjecture.
In abstract algebra, Jacobson's conjecture is an open problem in ring theory concerning the intersection of powers of the Jacobson radical of a Noetherian ring.
Georgia McClure Benkart was an American mathematician who was known for her work in the structure and representation theory of Lie algebras and related algebraic structures. She published over 130 journal articles and co-authored three American Mathematical Society memoirs in four broad categories: modular Lie algebras; combinatorics of Lie algebra representations; graded algebras and superalgebras; and quantum groups and related structures.
Amnon Yekutieli is an Israeli mathematician, working in noncommutative algebra, algebraic geometry and deformation quantization. He is a professor of mathematics at the Ben-Gurion University of the Negev.
Lauren Kiyomi Williams is an American mathematician known for her work on cluster algebras, tropical geometry, algebraic combinatorics, amplituhedra, and the positive Grassmannian. She is Dwight Parker Robinson Professor of Mathematics at Harvard University.
Kevin Mor McCrimmon is an American mathematician, specializing in Jordan algebras. He is known for his introduction of quadratic Jordan algebras in 1966.
Marie A. Vitulli is an American mathematician and professor emerita at the University of Oregon.
David Kent Harrison was an American mathematician, specializing in algebra, particularly homological algebra and valuation theory.
Mikael Rørdam is a Danish mathematician, specializing in the theory of operator algebras and its applications.
Jan Saxl was a Czech-British mathematician, and a professor at the University of Cambridge. He was known for his work in finite group theory, particularly on consequences of the classification of finite simple groups.
Wallace Smith Martindale III is an American mathematician, known for Martindale's Theorem (1969) and the Martindale ring of quotients introduced in the proof of the theorem. His 1969 paper generalizes Posner's theorem and a theorem of Amitsur and gives an independent, unified proof of the two theorems.
Louxin Zhang is a Canadian computational biologist. He is currently a professor in the Department of Mathematics at the National University of Singapore. He is recognized for his contributions to combinatorial semigroup theory in mathematics. In addition, he is recognized for his work on the mathematical understanding of phylogenetic trees and networks, as well as the analysis of spaced seeds for sequence comparison in bioinformatics.
