Composition Series

A composition series of an object A in an abelian category is a sequence of subobjects

such that each quotient object Xi /Xi + 1 is simple (for 0 ≤ i < n). If A has a composition series, the integer n only depends on A and is called the length of A.

Famous quotes containing the words composition and/or series:

    “I live in the angle of a leaden wall, into whose composition was poured a little alloy of bell-metal. Often, in the repose of my mid-day, there reaches my ears a confused tintinnabulum from without. It is the noise of my contemporaries.”
    —Henry David Thoreau (1817–1862)

    “There is in every either-or a certain naivete which may well befit the evaluator, but ill- becomes the thinker, for whom opposites dissolve in series of transitions.”
    —Robert Musil (1880–1942)