Let be a collection of modules in some category of modules. Then the direct sum of that collection is the submodule of the direct product (http://planetmath.org/DirectProduct) of the consisting of all elements such that all but a finite number of the are zero.
The direct sum is often referred to as the weak direct sum or simply the sum.
Compare this to the direct product of modules.
Often an internal direct sum is written as .
|Date of creation||2013-03-22 12:09:37|
|Last modified on||2013-03-22 12:09:37|
|Last modified by||antizeus (11)|
|Synonym||weak direct sum|