Indecomposable Module (original) (raw)
TOPICS
Algebra Applied Mathematics Calculus and Analysis Discrete Mathematics Foundations of Mathematics Geometry History and Terminology Number Theory Probability and Statistics Recreational Mathematics Topology
Alphabetical Index New in MathWorld
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, 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
See also
This entry contributed by Margherita Barile
Explore with Wolfram|Alpha
More things to try:
References
Rowen, L. "Indecomposable Modules and LE-Modules." ยง2.9 in Ring Theory, Vol. 1. San Diego, CA: Academic Press, pp. 237-261, 1988.
Referenced on Wolfram|Alpha
Cite this as:
Barile, Margherita. "Indecomposable Module." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/IndecomposableModule.html