Module Length
The length of all composition series of a module M. According to the Jordan-Hölder theorem for modules, if M has any composition series, then all such series are equivalent. The length of a module without composition series is conventionally set equal to infty.
A module has finite length iff it is both Artinian and Noetherian; this includes the case where M is finite.
An abstract vector space has finite length iff it is finite-dimensional, and in this case the length coincides with the dimension.
See also
Composition Series, Dimension, Jordan-Hölder TheoremThis entry contributed by Margherita Barile
Explore with Wolfram|Alpha
WolframAlpha
More things to try:
References
Atiyah, M. F. and Macdonald, I. G. Introduction to Commutative Algebra. Menlo Park, CA: Addison-Wesley, pp. 76-78, 1969.Referenced on Wolfram|Alpha
Module LengthCite this as:
Barile, Margherita. "Module Length." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/ModuleLength.html