WEEKLY ACTIVITIES

Time: 10h30, Wednesday, March 9, 2016
Location: Room 6, Building A14, Institute of Mathematics, 18 Hoang Quoc Viet, Cau Giay, Hanoi
Abstract: A ring $R$ is called left pure semisimple if every left $R$-module is a direct sum of finitely generated left $R$-modules, or equivalently, if $R$ has left pure global dimension zero. It is well known that a ring $R$ is left and right pure semisimple if and only if $R$ is of finite representation type, i.e. $R$ is (left and right) artinian  with only finitely many non-isomorphic finitely generated indecomposable (left and right) modules. The problem whether left pure semisimple rings are always of finite representation type, known as the pure semisimplicity conjecture, has been open since 1970s. In this talk, we present a brief survey on the history, and some recent progress on this problem.