operation that pairs a left and a right 𝑅‐module into an abelian group
\begin{aligned}M\otimes_RN&=(M\otimes_{\mathbb Z}N)/I\\I&=(m\otimes_{\mathbb Z}rn-mr\otimes_{\mathbb Z}n\colon m\in M,\,n\in N,\;r\in R)\end{aligned}