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:
“As to the rout that is made about people who are ruined by extravagance, it is no matter to the nation that some individuals suffer. When so much general productive exertion is the consequence of luxury, the nation does not care though there are debtors in gaol; nay, they would not care though their creditors were there too.”
—Samuel Johnson (1709–1784)
“Can a woman become a genius of the first class? Nobody can know unless women in general shall have equal opportunity with men in education, in vocational choice, and in social welcome of their best intellectual work for a number of generations.”
—Anna Garlin Spencer (1851–1931)
“At that,
his small size,
keen eyes,
serviceable beak
and general truculence
assure his survival—”
—William Carlos Williams (1883–1963)