Definition of direct sum in English:

direct sum


  • A set regarded formally as the sum of sets X₁,…, Xₙ, consisting of ordered n -tuples (x₁,…, xₙ), where xᵢ ∈ Xᵢ, and distinguished from a direct product only in the case of an infinite number of sets, the direct sum consisting only of sequences containing a finite number of non-zero elements.


Early 20th century; earliest use found in Proceedings of the London Mathematical Society.