any algebraic structures and of the same kind.

The direct sum of finitely many abelian groups, vector spaces, or modules is canonically isomorphic to the corresponding direct product. That is false, however, for some algebraic objects like nonabelian groups.

In the case where infinitely many objects are combined, the direct sum and direct product are not isomorphic even for abelian groups, vector spaces, or modules. For example, consider the direct

1.Previous
3.Next