Direct sum

Common card · No. 253592

In mathematics, more specifically in algebra, the direct sum of a collection of abelian groups is an abelian group constructed by combining the given groups as described below. If the input abelian groups have additional structure (for example, are vector spaces, modules, or topological abelian groups), then the direct sum usually maintains that structure (as an example of the opposite, the direct sum of fields is not a field as it contains zero divisors). The direct sum of two abelian groups A {\displaystyle A} and B {\displaystyle B} is another abelian group A ⊕ B {\displaystyle A\oplus B} consisting of the ordered pairs ( a , b ) {\displaystyle (a,b)} where a ∈ A {\displaystyle a\in A} and...

Read on Wikipedia