In mathematics, the Kurosh problem is one general problem, and several more special questions, in ring theory. The general problem is known to have a negative solution, since one of the special cases has been shown to have counterexamples. These matters were brought up by Aleksandr Gennadievich Kurosh as analogues of the Burnside problem in group theory.
Kurosh asked whether there can be a finitely-generated infinite-dimensional algebraic algebra (the problem being to show this cannot happen). A special case is whether or not every nil algebra is locally nilpotent.
For PI-algebras the Kurosh problem has a positive solution.
Golod showed a counterexample to that case, as an application of the Golod–Shafarevich theorem.
The Kurosh problem on group algebras concerns the augmentation ideal I. If I is a nil ideal, is the group algebra locally nilpotent?
There is an important problem which is often referred as the Kurosh's problem on division rings. The problem asks whether there exists an algebraic (over the center) division ring which is not locally finite. This problem has not been solved until now.
In mathematics, the Kuroshproblem is one general problem, and several more special questions, in ring theory. The general problem is known to have a negative...
Aleksandr Gennadyevich Kurosh (Russian: Алекса́ндр Генна́диевич Ку́рош; January 19, 1908 – May 18, 1971) was a Soviet mathematician, known for his work...
the Kurosh subgroup theorem and Kuroshproblem in group theory Olga Ladyzhenskaya, made major contributions to solution of Hilbert's 19th problem and...
theorem and describing function Aleksandr Kurosh, author of the Kurosh subgroup theorem and Kuroshproblem in group theory Olga Ladyzhenskaya, made major...
Hilbert O. Hölder B. Huppert K. Iwasawa Z. Janko C. Jordan F. Klein A. Kurosh J.L. Lagrange C. Leedham-Green F.W. Levi Sophus Lie W. Magnus E. Mathieu...
Lyndon–Shirshov words, Hall–Shirshov bases, Shirshov's Theorem on the Kuroshproblem for alternative and Jordan algebras, and Shirshov's Theorem on the speciality...
Alexandrov, the most famous are Lev Pontryagin, Andrey Tychonoff and Aleksandr Kurosh. The older generation of his students includes L. A. Tumarkin, V. V. Nemytsky...
representation of the divine and the numinous in early Achaemenid Iran: old problems, new directions; Mark A. Garrison, Trinity University, San Antonio, Texas;...
solution to the Kurosh–Levitzky problem on the nilpotency of finitely generated nil algebras, and so to a weak form of Burnside's problem. Golod was a student...
Bounded variation Caccioppoli set Differential equation on a graph See Kurosh et al. (1959b, p. 145). See Fomin & Shilov (1969, p. 265). According to...
papers by Nikol'skii, Privalov and Ul'yanov (1984, p. 180; 1986, p. 156). Kurosh, A. G.; Vityushkov, V. I.; Boltyanskii, V. G.; Dynkin, E. B.; Shilov, G...
abelian groups of arbitrary cardinality (in Russian), Mat. Sb., 16 (1945), 129–162 Kurosh, A. G. (1960), The theory of groups, New York: Chelsea, MR 0109842...
the Ural Industrial Institute under the outside tutelage of Alexandr G. Kurosh (of the University of Moscow). A remarkable student, Chernikov was made...
State University in 1947 under the supervision of Aleksandr Gennadievich Kurosh and Otto Schmidt. Radicals of algebras and structure theory (with Iu. M...
(Mikhlin 1968, p. 4). See the report of the conference by Aleksandrov & Kurosh (1959, p. 250). Almost all recollections of Gaetano Fichera concerning how...
Ladyzhenskaya James Serrin See (Kurosh et al. 1959, p. 237). See (Serrin 1959, p. 251, footnote 1) and (Serrin 1959b, p. 271). Kurosh et al. (1959, p. 237) precisely...
close version of Grushko's original proof is given in the 1955 book of Kurosh. Like the original proofs, Lyndon's proof (1965) relied on length-functions...
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