In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers. The prime ideals for the integers are the sets that contain all the multiples of a given prime number, together with the zero ideal.
In mathematics, more specifically ring theory, the Jacobson radical of a ring R is the ideal consisting of those elements in R that annihilate all simple right R-modules. It happens that substituting "left" in place of "right" in the definition yields the same ideal, and so the notion is left–right symmetric. The Jacobson radical of a ring is frequently denoted by J(R) or rad(R); the former notation will be preferred in this article, because it avoids confusion with other radicals of a ring. The Jacobson radical is named after Nathan Jacobson, who was the first to study it for arbitrary rings in Jacobson 1945.
In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers. Ring theory studies the structure of rings, their representations, or, in different language, modules, special classes of rings, as well as an array of properties that proved to be of interest both within the theory itself and for its applications, such as homological properties and polynomial identities.
John Henry Constantine Whitehead FRS, known as "Henry", was a British mathematician and was one of the founders of homotopy theory. He was born in Chennai, in India, and died in Princeton, New Jersey, in 1960.
Sir Martin John Taylor, FRS is a British mathematician and academic. He was Professor of Pure Mathematics at the School of Mathematics, University of Manchester and, prior to its formation and merger, UMIST where he was appointed to a chair after moving from Trinity College, Cambridge in 1986. He was elected Warden of Merton College, Oxford on 5 November 2009, took office on 2 October 2010 and retired in September 2018.
In mathematics, the Köthe conjecture is a problem in ring theory, open as of 2022. It is formulated in various ways. Suppose that R is a ring. One way to state the conjecture is that if R has no nil ideal, other than {0}, then it has no nil one-sided ideal, other than {0}.
In mathematics, more specifically ring theory, a left, right or two-sided ideal of a ring is said to be a nil ideal if each of its elements is nilpotent.
Irving Kaplansky was a mathematician, college professor, author, and amateur musician.
Peter Jephson Cameron FRSE is an Australian mathematician who works in group theory, combinatorics, coding theory, and model theory. He is currently half-time Professor of Mathematics at the University of St Andrews, and Emeritus Professor at Queen Mary University of London.
In algebra, the term Hermite ring has been applied to three different objects.
Richard Paul Winsley Thomas is a British mathematician working in several areas of geometry. He is a professor at Imperial College London. He studies moduli problems in algebraic geometry, and ‘mirror symmetry’—a phenomenon in pure mathematics predicted by string theory in theoretical physics.
Claudio Procesi is an Italian mathematician, known for works in algebra and representation theory.
Daniela Kühn is a German mathematician and the Mason Professor in Mathematics at the University of Birmingham in Birmingham, England. She is known for her research in combinatorics, and particularly in extremal combinatorics and graph theory.
Iain Gordon, FRSE, is a mathematician, currently Iain Gordon is Professor of Mathematics, Vice-Principal and Head of the College of Science and Engineering at the University of Edinburgh. His field of specialisation is representation theory and noncommutative algebra.
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.
Klaus Wilhelm Roggenkamp was a German mathematician, specializing in algebra.
Aderemi Oluyomi Kuku was a Nigerian mathematician and academic, known for his contributions to the fields of algebraic K-theory and non-commutative geometry. Born in Ijebu-Ode, Ogun State, Nigeria, Kuku began his academic journey at Makerere University College and the University of Ibadan, where he earned his B.Sc. in Mathematics, followed by his M.Sc. and Ph.D. under Joshua Leslie and Hyman Bass. His doctoral research focused on the Whitehead group of p-adic integral group-rings of finite p-groups. Kuku held positions as a lecturer and professor at various Nigerian universities, including the University of Ife and the University of Ibadan, where he served as Head of the Department of Mathematics and Dean of the Postgraduate School. His research involved developing methods for computing higher K-theory of non-commutative rings and articulating higher algebraic K-theory in the language of Mackey functors. His work on equivariant higher algebraic K-theory and its generalisations impacted the field.
Martha Bettina Richmond was a German-American mathematician, mathematics textbook author, professor at Western Kentucky University, and murder victim.
