Top (algebra)

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) R, 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.

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