Direct Summand

Given the direct sum of additive Abelian groups A direct sum B, A and B are called direct summands. The map i_1:A-->A direct sum B defined by i(a)=a direct sum 0 is called the injection of the first summand, and the map p_1:A direct sum B-->A defined by p_1(a direct sum 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.

See also

Direct Factor, Direct Sum, Module Direct Sum

This entry contributed by Margherita Barile

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Cite this as:

Barile, Margherita. "Direct Summand." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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