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:
“Modern Western thought will pass into history and be incorporated in it, will have its influence and its place, just as our body will pass into the composition of grass, of sheep, of cutlets, and of men. We do not like that kind of immortality, but what is to be done about it?”
—Alexander Herzen (1812–1870)
“Every Age has its own peculiar faith.... Any attempt to translate into facts the mission of one Age with the machinery of another, can only end in an indefinite series of abortive efforts. Defeated by the utter want of proportion between the means and the end, such attempts might produce martyrs, but never lead to victory.”
—Giuseppe Mazzini (1805–1872)