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:
“I make this direct statement to the American people that there is far less chance of the United States getting into war, if we do all we can now to support the nations defending themselves against attack by the Axis than if we acquiesce in their defeat, submit tamely to an Axis victory, and wait our turn to be the object of attack in another war later on.”
—Franklin D. Roosevelt (1882–1945)
“No, the five hundred was the sum they named
To pay the doctor’s bill and tide me over.
It’s that or fight, and I don’t want to fight
I just want to get settled in my life....”
—Robert Frost (1874–1963)
“‘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)