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...

can be used to form the direct sum of two vector spaces or two modules. We can also form direct sums with any finite number of summands, for example A...

groups can be generalized to direct sums of vector spaces, modules, and other structures; see the article direct sum of modules for more information. A group...

objects Direct sum of groups Direct sum of modules Direct sum of permutations Direct sum of topological groups Einstein summation, a way of contracting...

the free product of groups, and the direct sum of modules and vector spaces. The coproduct of a family of objects is essentially the "least specific"...

up direct in Wiktionary, the free dictionary. Direct may refer to: Directed set, in order theory Direct limit of (pre), sheaves Direct sum of modules, a...

decomposition of a module is a way to write a module as a direct sum of modules. A type of a decomposition is often used to define or characterize modules: for...

decomposition into a direct sum of copies of R (rank one free modules) is replaced by a direct sum into rank one projective modules: the individual summands...

irreducible. Semisimple A semisimple module is a direct sum (finite or not) of simple modules. Historically these modules are also called completely reducible...

every injective module is uniquely a direct sum of indecomposable modules, and their structure is well understood. An injective module over one ring, may...