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:
“Mr. Chadband is a large yellow man, with a fat smile, and a general appearance of having a good deal of train oil in his system.”
—Charles Dickens (1812–1870)
“They make a great ado nowadays about hard times; but I think that ... this general failure, both private and public, is rather occasion for rejoicing, as reminding us whom we have at the helm,—that justice is always done. If our merchants did not most of them fail, and the banks too, my faith in the old laws of the world would be staggered.”
—Henry David Thoreau (1817–1862)
“The general will is always right.”
—Jean-Jacques Rousseau (1712–1778)