Given the direct sum of additive Abelian groups A⊕B, A and B are called direct summands. The map i_1 :A⟶A⊕B defined by i(a) = a⊕0 is called the injection of the first summand, and the map p_1 :A⊕B⟶A defined by p_1(a⊕b) = a is called the projection onto the first summand. Similar maps i_2, p_2 are defined for the second summand B. The above definitions extend in a natural way to the direct sums of more than two Abelian groups.

direct factor | direct sum | module direct sum