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:
“The general interest of the masses might take the place of the insight of genius if it were allowed freedom of action.”
—Denis Diderot (1713–1784)
“Women born at the turn of the century have been conditioned not to speak openly of their wedding nights. Of other nights in bed with other men they speak not at all. Today a woman having bedded with a great general feels free to tell us that in bed the general could not present arms. Women of my generation would have spared the great general the revelation of this failure.”
—Jessamyn West (1907–1984)
“The most general deficiency in our sort of culture and education is gradually dawning on me: no one learns, no one strives towards, no one teaches—enduring loneliness.”
—Friedrich Nietzsche (1844–1900)