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:
“Give a scientist a problem and he will probably provide a solution; historians and sociologists, by contrast, can offer only opinions. Ask a dozen chemists the composition of an organic compound such as methane, and within a short time all twelve will have come up with the same solution of CH4. Ask, however, a dozen economists or sociologists to provide policies to reduce unemployment or the level of crime and twelve widely differing opinions are likely to be offered.”
—Derek Gjertsen, British scientist, author. Science and Philosophy: Past and Present, ch. 3, Penguin (1989)
“The professional celebrity, male and female, is the crowning result of the star system of a society that makes a fetish of competition. In America, this system is carried to the point where a man who can knock a small white ball into a series of holes in the ground with more efficiency than anyone else thereby gains social access to the President of the United States.”
—C. Wright Mills (1916–1962)