(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Show that [itex]\mathbb{Z}_{10}\otimes_{\mathbb{Z}}\mathbb{Z}_{12} \cong \mathbb{Z}_{2}[/itex]

3. 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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# Homework Help: Simple Tensor Product

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