Direct Sum of Rings
Given a finite family of rings R1, ..., Rn, the direct product of the Ri is sometimes called the direct sum.
Note that in the category of commutative rings, the direct sum is not the coproduct. Instead, the coproduct is the tensor product of rings.
Read more about this topic: Direct Sum
Famous quotes containing the words direct, sum and/or rings:
“One merit in Carlyle, let the subject be what it may, is the freedom of prospect he allows, the entire absence of cant and dogma. He removes many cartloads of rubbish, and leaves open a broad highway. His writings are all unfenced on the side of the future and the possible. Though he does but inadvertently direct our eyes to the open heavens, nevertheless he lets us wander broadly underneath, and shows them to us reflected in innumerable pools and lakes.”
—Henry David Thoreau (1817–1862)
“the possibility of rule as the sum of rulelessness:”
—Archie Randolph Ammons (b. 1926)
“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)