Search

The Jacobson radical of a ring was first formally studied in 1945 by Nathan Jacobson and is an important object in modern abstract algebra. The analogous notion of the Jacobson radical for a module is referred to as the radical of a module. The radical of a module is the intersection of all its maximal submodules. Often, the radical of a module is superfluous to the behavior of the module itself and also contains important information about the module. The study of the radical of a module often appears as part of other investigations. This thesis represents work towards understanding the radical of a module extension. Given a ring R and R-modules A,B,X such that X is an extension of B by A as in the short exact sequence