Direct sum of modules
Operation in abstract algebra / From Wikipedia, the free encyclopedia
Dear Wikiwand AI, let's keep it short by simply answering these key questions:
Can you list the top facts and stats about Direct sum of modules?
Summarize this article for a 10 year old
In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which is the dual notion.
The most familiar examples of this construction occur when considering vector spaces (modules over a field) and abelian groups (modules over the ring Z of integers). The construction may also be extended to cover Banach spaces and Hilbert spaces.
See the article decomposition of a module for a way to write a module as a direct sum of submodules.