A non-zero module which is not the direct sum of two of its proper submodules. The negation of indecomposable is, of course, decomposable. An abstract vector space is indecomposable iff it has dimension 1.
As a consequence of Kronecker basis theorem, an Abelian group is indecomposable iff it is either isomorphic to or to , where is a prime power. This is not the case for , and in fact we have