Algebra Seminar

Wednesday, April 19, 2017 3:30 pm - 3:30 pm EDT (GMT -04:00)

Be'eri Greenfeld, Bar Ilan University

"Around and beyond the Koethe problem"

Suppose we are given two left ideals L,L' in some ring, and suppose these are nil ideals (namely, every element in each one of them, raised to some power, vanishes). Must L+L' be nil? This looking innocent question was posed by Koethe in 1930. Since then, it has become a major open problem in ring theory, due to its many equivalent (sometimes surprisingly) formulations, thereby motivating a flurry of research with tools and applications from classical ring theory, group theory, combinatorics of words, geometry etc.

The aim of this talk is to draw an accurate (as much as time permits) picture of the original problem and its equivalent formulations, and to trace the ramifications each one of them led ring theorists to, during the last 80 years. We will also discuss problems and results inspired from the Koethe problem, e.g. for differential polynomial rings, graded algebras and various radicals.

MC 5403