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:

    For man is not the creature and product of Mechanism; but, in a far truer sense, its creator and producer.
    Thomas Carlyle (1795–1881)

    Poetry is the only life got, the only work done, the only pure product and free labor of man, performed only when he has put all the world under his feet, and conquered the last of his foes.
    Henry David Thoreau (1817–1862)

    ‘She has got rings on every finger,
    Round one of them she have got three.
    She have gold enough around her middle
    To buy Northumberland that belongs to thee.
    Unknown. Young Beichan (l. 61–64)