High Quality Content by WIKIPEDIA articles! In the context of a module M over a ring R, the top of M is the largest semisimple quotient module of M if it exists.For finite-dimensional k-algebras (k a field), if rad(M) denotes the intersection of all proper maximal submodules of M (the radical of the module), then the top of M is M/rad(M). In the case of local rings with maximal ideal P, the top of M is M/PM. In general if R is semi-artinian (that is, if R/Rad(R) is an Artinian ring, where Rad(R) is the Jacobson radical of R), then M/rad(M) is a semisimple module and is the top of M. This includes the cases of local rings and finite dimensional algebras over fields.

Данное издание не является оригинальным. Книга печатается по технологии принт-он-деманд после получения заказа.