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:
“Much of our American progress has been the product of the individual who had an idea; pursued it; fashioned it; tenaciously clung to it against all odds; and then produced it, sold it, and profited from it.”
—Hubert H. Humphrey (1911–1978)
“These facts have always suggested to man the sublime creed that the world is not the product of manifold power, but of one will, of one mind; and that one mind is everywhere active, in each ray of the star, in each wavelet of the pool; and whatever opposes that will is everywhere balked and baffled, because things are made so, and not otherwise.”
—Ralph Waldo Emerson (1803–1882)
“The next time the novelist rings the bell I will not stir though the meeting-house burn down.”
—Henry David Thoreau (1817–1862)