direct product of modules (original) (raw)

For each j∈I we have a projection pj:∏i∈IXi→Xjdefined by (xi)↦xj, and an injection λj:Xj→∏i∈IXiwhere an element xj of Xjmaps to the element of ∏i∈IXiwhose jth term is xj and every other term is zero.

The direct product is often referred to as the complete direct sum, or the strong direct sum, or simply the .

Compare this to the direct sum of modules.