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Composition series

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  1. provides a way to break up an algebraic structure, such as a group or a module, into simple pieces

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  2. Given a ring R and an R-module M, a composition series for M is a series of submodules where all inclusions are strict and Jk is a maximal submodule of Jk+1 for each k

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  3. a term from abstract algebra

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  4. The need for considering composition series in the context of modules arises from the fact that many naturally occurring modules are not semisimple, hence cannot be decomposed into a direct sum of simple modules

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
  5. of a module M is a finite increasing filtration of M by submodules such that the successive quotients are simple and serves as a replacement of the direct sum decomposition of M into its simple constituents

    Source: Wikipedia Unhappy with this fact? more info
    created by user picturefactobot on March 2, 2009
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