02.05.2016-13.05.2016: Alexei Kanel-Belov.
Exposé le mardi 3.5.2016 à 14h00, salle U ou V: On geometric ring theory
Résumé: Quite recently Ilia Rips and Arieh Juhasz constructed an Engel but not locally nilpotent group, i.e. a group with identities $[\dots[x,y],y,\dots,y]=e$. This group has non-positive curvature and big commutative parts: some parts have small cancellation and some commute. --- This group looks somehow like a ring and group multiplication sometimes behaves like multiplication and sometimes like addition. The theory of canonic forms of this group is applicable for rings in particular in the skew field construction.
Note also that rings are close to semigroups too. There is a hope nowdays to develop geometric ring theory.