The Tensor Product As Ring
To get a general theory, one needs to consider a ring structure on . One can define the product to be . This formula is multilinear over N in each variable; and so defines a ring structure on the tensor product, making into a commutative N-algebra, called the tensor product of fields.
Read more about this topic: Tensor Product Of Fields
Famous quotes containing the words product and/or ring:
“The UN is not just a product of do-gooders. It is harshly real. The day will come when men will see the UN and what it means clearly. Everything will be all right—you know when? When people, just people, stop thinking of the United Nations as a weird Picasso abstraction, and see it as a drawing they made themselves.”
—Dag Hammarskjöld (1905–1961)
“Close friends contribute to our personal growth. They also contribute to our personal pleasure, making the music sound sweeter, the wine taste richer, the laughter ring louder because they are there.”
—Judith Viorst (20th century)