In mathematics, specifically abstract algebra, an Artinian ring is a ring that satisfies the descending chain condition on (one-sided) ideals; that is, there is no infinite descending sequence of ideals. Artinian rings are named after Emil Artin, who first discovered that the descending chain condition for ideals simultaneously generalizes finite rings and rings that are finite-dimensional vector spaces over fields. The definition of Artinian rings may be restated by interchanging the descending chain condition with an equivalent notion: the minimum condition.
Michael Artin is a German-American mathematician and a professor emeritus in the Massachusetts Institute of Technology Mathematics Department, known for his contributions to algebraic geometry.
The Nansen Medal for Outstanding Research is a Norwegian medal awarded by the Nansen Fund.
In algebra, an Artin algebra is an algebra Λ over a commutative Artin ring R that is a finitely generated R-module. They are named after Emil Artin.
Maurice Auslander was an American mathematician who worked on commutative algebra, homological algebra and the representation theory of Artin algebras. He proved the Auslander–Buchsbaum theorem that regular local rings are factorial, the Auslander–Buchsbaum formula, and, in collaboration with Idun Reiten, introduced Auslander–Reiten theory and Auslander algebras.
In algebra, Auslander–Reiten theory studies the representation theory of Artinian rings using techniques such as Auslander–Reiten sequences and Auslander–Reiten quivers. Auslander–Reiten theory was introduced by Maurice Auslander and Idun Reiten and developed by them in several subsequent papers.
In algebra, a triangular matrix ring, also called a triangular ring, is a ring constructed from two rings and a bimodule.
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.
Eric Mark Friedlander is an American mathematician who is working in algebraic topology, algebraic geometry, algebraic K-theory and representation theory.
Ruth Michele Charney is an American mathematician known for her work in geometric group theory and Artin groups. Other areas of research include K-theory and algebraic topology. She holds the Theodore and Evelyn G. Berenson Chair in Mathematics at Brandeis University. She was in the first group of mathematicians named Fellows of the American Mathematical Society. She was in the first group of mathematicians named Fellows of the Association for Women in Mathematics. She served as president of the Association for Women in Mathematics during 2013–2015, and served as president of the American Mathematical Society for the 2021–2023 term.
Tamar Debora Ziegler is an Israeli mathematician known for her work in ergodic theory, combinatorics and number theory. She holds the Henry and Manya Noskwith Chair of Mathematics at the Einstein Institute of Mathematics at the Hebrew University.
Tatiana Toro is a Colombian-American mathematician at the University of Washington. Her research is "at the interface of geometric measure theory, harmonic analysis and partial differential equations". Toro was appointed director of the Simons Laufer Mathematical Sciences Institute for 2022–2027.
Bernhard Keller is a Swiss mathematician, specializing in algebra. He is a professor at the University of Paris.
Catharina Stroppel is a German mathematician whose research concerns representation theory, low-dimensional topology, and category theory. She is a professor of mathematics at the University of Bonn, and vice-coordinator of the Hausdorff Center for Mathematics in Bonn.
Zoé Maria Chatzidakis is a mathematician who works as a director of research at the École Normale Supérieure in Paris, France. Her research concerns model theory and difference algebra. She was invited to give the Tarski Lectures in 2020, though the lectures were postponed due to the COVID-19 pandemic.
Christine Riedtmann is a Swiss mathematician specializing in abstract algebra. She earned her PhD in 1978 from the University of Zurich under the supervision of Pierre Gabriel, and is a professor emeritus at the University of Bern.
Gabriele Vezzosi is an Italian mathematician, born in Florence, Italy. His main interest is algebraic geometry.
Marc N. Levine is an American mathematician.
Gordana Todorov is a mathematician working in noncommutative algebra, representation theory, Artin algebras, and cluster algebras. She is a professor of mathematics at Northeastern University.
Andrei Vladimirovich Roiter was a Ukrainian mathematician, specializing in algebra.
