Product of Rings

Product Of Rings

In mathematics, it is possible to combine several rings into one large product ring. This is done as follows: if I is some index set and Ri is a ring for every i in I, then the cartesian product Πi in I Ri can be turned into a ring by defining the operations coordinate-wise.

The resulting ring is called a direct product of the rings Ri. The direct product of finitely many rings coincides with the direct sum of rings.

Read more about Product Of Rings:  Examples, Properties

Famous quotes containing the words product of, product and/or rings:

    The product of mental labor—science—always stands far below its value, because the labor-time necessary to reproduce it has no relation at all to the labor-time required for its original production.
    Karl Marx (1818–1883)

    The writer’s language is to some degree the product of his own action; he is both the historian and the agent of his own language.
    Paul De Man (1919–1983)

    Ye say they all have passed away,
    That noble race and brave;
    That their light canoes have vanished
    From off the crested wave;
    That, mid the forests where they roamed,
    There rings no hunters’ shout;
    But their name is on your waters,
    Ye may not wash it out.
    Lydia Huntley Sigourney (1791–1865)