Re: Need Example of Tensor product

Patt wrote:
Is there anyone give me an example of the following statement? The
element u in A x_R B such that u is not equal to a x_R b for a in A
and b in B where x_R denote the tensor product over ring R. Thank you.


Consider the case where A and B are R^2, and R is, well, R (the reals).
What is A tensor B? What is the rank of any element of the form
a tensor b? Can you now think of an element of A tensor B which
is not of the form a tensor b?
.

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