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- Jun 22, 2012

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In Section 10.4, Example 3 (see attachment) , Dummit and Foote where we are dealing with the tensor product \(\displaystyle \mathbb{Z} / m \mathbb{Z} \otimes \mathbb{Z} / n \mathbb{Z}\) we find the following statement: (NOTE: d is the gcd of integers m and n)

"Since \(\displaystyle m(1 \otimes 1) = m \otimes 1 = 0 \otimes 1 = 0 \)

and similarly

\(\displaystyle n(1 \otimes 1) = 1 \otimes n = 1 \otimes 0 = 0 \)

we have

\(\displaystyle d(1 \otimes 1) = 0 \) ... ... "

Basically we have

mx = 0 and nx = 0 and have to show dx = 0

It must be simple but I cannot see it!

Can someone please help?

Peter