Suppose I have $R$ a ring, and let M,N be two $R$-bimodules.
Suppose I have $$ (m_1 \otimes_Rn_1)=(m_2 \otimes_R n_2). $$
Then what can I say about $m_1$ and $m_2$ and, respectively, $n_1$ and $n_2$?
Thanks!
2026-04-21 21:09:10.1776805750
When are two elementary tensor equal
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In general you can not say anything, since you can think for two modules when you tensor them get zero. Take any two elements both should be equal but there are no relation between them. For example take $M=Z_2$ , $N=Z_3$ it is clearly that $$(Z_2\otimes_R Z_3)=0$$.