Isomorphism Theorem - General

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:

    Private property is held sacred in all good governments, and particularly in our own. Yet shall the fear of invading it prevent a general from marching his army over a cornfield or burning a house which protects the enemy? A thousand other instances might be cited to show that laws must sometimes be silent when necessity speaks.
    Andrew Jackson (1767–1845)

    A general loathing of a gang or sect usually has some sound basis in instinct.
    Ezra Pound (1885–1972)

    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)