Alexander Mikhalev, Moscow State University

Abstract:
This talk is based on the recent research project "Radicals of associative rings, radicals of linear groups over rings, radicals of Lie algebras" by A.U.Golubkov, A.V.Mikhalev, S.A.Pihtilkov. The main goal is just to have a look at old and new results around the Golubchik-Mikhalev formula for prime radical of the general linear group over an arbitrary associative ring. The prime radical (for rings, groups, Lie algebras) is under consideration in connection with some other radicals close to it. As an application of this technique we show some recent solutions of open problems.