- #1
Kindayr
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Homework Statement
Show that [itex]\mathbb{Z}_{10}\otimes_{\mathbb{Z}}\mathbb{Z}_{12} \cong \mathbb{Z}_{2}[/itex]
The Attempt at a Solution
Clearly, for any [itex]0\neq m\in\mathbb{Z}_{10}[/itex] and [itex]0\neq n \in \mathbb{Z}_{12}[/itex] we have that [itex]m\otimes n = mn(1\otimes 1)[/itex], and if either [itex]m=0[/itex] or [itex]n=0[/itex] we have that [itex]m\otimes n = 0\otimes 0[/itex].
I just don't know how to finish it.
I'm just working through Vakil's Algebraic Geometry monograph for fun, and this seemingly trivial question is bothering me.
Thank you for any help!
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