An indecomposable module is a non-zero module which is not the direct sum of two of its proper submodules. The negation of indecomposable is decomposable. An abstract vector space is indecomposable iff it has dimension 1.

As a consequence of Kronecker basis theorem, a finitely generated 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

See also

Indecomposable

Portions of this entry contributed by Margherita Barile

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References

Rowen, L. "Indecomposable Modules and LE-Modules." §2.9 in Ring Theory, Vol. 1. San Diego, CA: Academic Press, pp. 237-261, 1988.

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Indecomposable Module

Cite this as:

Weisstein, Eric W., with contributions by Margherita Barile. "Indecomposable Module." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/IndecomposableModule.html

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