Examples
The zero module is the only one with length 0. Modules with length 1 are precisely the simple modules.
For every finite-dimensional vector space (viewed as a module over the base field), the length and the dimension coincide.
The length of the cyclic group Z/nZ (viewed as a module over the integers Z) is equal to the number of prime factors of n, with multiple prime factors counted multiple times.
Read more about this topic: Length Of A Module
Famous quotes containing the word examples:
“It is hardly to be believed how spiritual reflections when mixed with a little physics can hold people’s attention and give them a livelier idea of God than do the often ill-applied examples of his wrath.”
—G.C. (Georg Christoph)
“There are many examples of women that have excelled in learning, and even in war, but this is no reason we should bring ‘em all up to Latin and Greek or else military discipline, instead of needle-work and housewifry.”
—Bernard Mandeville (1670–1733)
“Histories are more full of examples of the fidelity of dogs than of friends.”
—Alexander Pope (1688–1744)