General
To generalise this to universal algebra, normal subgroups need to be replaced by congruences.
A congruence on an algebra is an equivalence relation which is a subalgebra of endowed with the component-wise operation structure. One can make the set of equivalence classes into an algebra of the same type by defining the operations via representatives; this will be well-defined since is a subalgebra of .
Read more about this topic: Isomorphism Theorem
Famous quotes containing the word general:
“That sort of half sigh, which, accompanied by two or three slight nods of the head, is pity’s small change in general society.”
—Charles Dickens (1812–1870)
“We have grown literally afraid to be poor. We despise anyone who elects to be poor in order to simplify and save his inner life. If he does not join the general scramble and pant with the money-making street, we deem him spiritless and lacking in ambition.”
—William James (1842–1910)
“A constitutional statesman is in general a man of common opinions and uncommon abilities.”
—Walter Bagehot (1826–1877)